I understand your frustration.  I'm in the same predicament.  Think of St. Monica who was St. Augustin's mother and how many years she had to pray for his conversion!  Take consolation in knowing that even the saints had to wait sometimes.  You might want to consider praying to her to intercede for you with God.  

The greatest thing you can do is have Masses said for their conversion.  This is what I've learned from books on Theology, the writings of the saints, and my Catholic education before Vatican II.  There is nothing better to offer to God the Father than the sufferings and death of His Son, which is what happens in the Mass.  

Next to that you can make the novena to the Sacred Heart which Padre Pio made.  It is available on the Internet.  I've made it and have received graces from doing so.  You can make the devotion of the First Fridays to which Jesus has attached many promises.  

The prayers of Our Lady come next as being the most powerful with God, for She is without sin and is the closest of all God's creatures to God Himself (a creature being defined as someone who is not God).  Her prayers are most efficacious.  The Rosary takes first place.  You can also say the Litany to Her to ask Her to intercede with God for this grace.  Also there is the Memorare which I think St. Bernard composed and it's very efficacious as well for obtaining graces.  

As for the saints, St. Joseph, of course, is powerful.  There is a litany to him.  Then there are Saints Jude and Rita who are known to be able to obtain graces from God for even "impossible" cases.  I believe the prayers to St. Jude require that you make known publicly that your prayer was answered, which you could do here on this forum.  

There is the Litany of All Saints where you call on the most powerful and well-known saints in heaven asking them to intercede for you for your intentions.  

You could pray to the patron saint of each person to ask for their conversion.

You could pray to the guardian angel of each person asking them to help that person be receptive to God's inspirations to amend their lives and help defend them from evil inclinations.

The key factor is that you have FAITH in God that He CAN give such a grace and CONFIDENCE that the grace will be given if God so wills.  And you must be willing to accept the fact that this grace or any grace for which you ask will be given when GOD thinks it best, which may not be when YOU think it best.  So perhaps God has agreed to answer your request but the conversions will take place only on their deathbeds.  This info is right from the books on Theology and the writings of the saints.  

You can also do other things such as practice mortifications and penances to go along with your prayers.  Christ said in the Gospels that some graces can only be obtained by "prayer and fasting."  

You can offer up all you do, every single thing you do that tends to the glory of God -- which is everything that is in line with the Commandments and the Evangelical Counsels of the Gospels -- and ask Jesus to unite your works with His when He was on this earth and He can offer them to God the Father for your intentions.  This is getting a little deeper into theology but again, it is recommended by the saints.  It has to do with us being members of the Mystical Body of Christ--spiritually we are united to Him by being in the state of grace and so we can use His merits to offer to God the Father for our requests.  You can also offer up His sufferings during His Passion for your intentions.  This is NOT the same as what the priest does at Mass.  You can find explanations of this in books written for nuns and priests before Vatican II.  That is what nuns used to do every day for the salvation and conversion of sinners, especially the cloistered nuns.  Prayer and penance for the salvation of souls and the good of the Church was their daily work, but this was not exclusively for nuns to do!  It's just that nuns devoted their time to it, as they had no obligations to family or a secular job, etc., which would prevent them from spending their lives this way.  Also, they had consecrated their virginity to God forever, which made them closer to God than non-consecrated people provided they lived what they professed to do.    

Our Faith is very rich with many, many devotions that have been used through the ages to obtain graces from God.  Unfortunately, since the Council devotion to the Mother of God and the saints has been de-emphasized because the new teachings say that everyone is okay, God is all-forgiving and we need not worry about His Justice and punishment for sin, no one needs to be converted, etc.  The old prayer books and instructional manuals have been thrown out or burned because they contradict this teaching, and those who were born and raised after Vatican II have little to no idea about these things and what treasures we had before the Council and how often people used these practices to obtain graces.  So your question is a very legitimate one.

But don't even start to feel overwhelmed by what I've written.  I'm just giving you suggestions.  What God looks for is a sincere heart and FAITH that He CAN do what you ask and that He WILL do what you ask provided He thinks it best.  And oftentimes He puts the desire into someone to make such a request as you are making so that He can give the desired grace.  He doesn't want people to go to hell.  He commands us to love our neighbor as we love ourselves.  We pray for our own salvation.  We should pray for the same for everyone, especially those whom He has placed in our life.  

There is no "magic prayer" as some may think.  But some prayers are more pleasing to God than others because of the person making them because those people are closer to God in holiness than we are and/or the prayers themselves contain more proper sentiments than we on our own may not express, such as an acknowledgement of our belief that He is powerful and good enough to listen to us and help us, that we are sinners and depend on Him for every good, etc.

An example of Someone Whom God loves greatly and always listens to is Our Lady for She is without sin; She was not conceived in Original Sin nor did She ever use Her free will to sin. She spent Her entire life only for the glory of God and doing His Will perfectly, so She has a very high place in heaven.

But God never turns away from a sincere heart asking with true Faith for help even if we forget to mention all the points that are contained in some formal prayers.  Witness the incidents in the Gospels where the centurion asked for help for his daughter and his faith was so strong that he told Jesus that He didn't even need to come to his home to see the girl, that he believed that all Jesus had to do was will for her to be healed and she would be--and she was.  Consider the woman who believed if she just touched the hem of His garment her hemorrhage would stop.  It did.  FAITH. God looks for FAITH.  

If you want specific prayers or litanies, let me know.  You can PM me.  I have many books to draw from and I just ordered a book of 200 litanies from before Vatican II.  I'd be glad to share with anyone.  I try to find things that were written before Vatican II in their original form and not reprints of the same thing which may have been edited to be more "correct" according to today's understanding.  

I hope you live to see your prayers answered.  At least know that God is pleased with your requesting this grace.  You will gain merit for doing so which will matter when you are judged and go towards your reward in eternity, according to the saints.  

Yes, Poche, absolutely!  I was an idiot to not mention these right at the top of  the list! So glad you did!  The poster's words had me thinking of litanies and other formal prayers.  It was later during my own prayer time that I realized I had forgotten to mention these specifically on their own apart from being part of the Rosary.

To the OP:  I also wanted to recommend the prayer book known as the Raccolta (which has indulgenced prayers) and prayer books by Fr. Lasance as good references for written prayers.  Both can be found online for free and were written before Vatican II.

Another thing I wanted to say is that I am not a priest so if you have a devout and knowledgeable priest to ask about these things, you should do so.  Any contribution I make to any topic comes from knowledge gained from 53 years of spiritual reading and study.  I have a large library but I've read so many books for so many years that I unfortunately cannot give specific citations as to where I learned this or that unless it's something I've read recently.  

I like to read books that were written for priests/seminarians and nuns because they give the most thorough explanations of the "how" and "why" of things, as well as the writings and sermons of the Doctors of the Church and the saints whom we know found favor with God because of the miracles obtained from prayer to them.  I don't trust any book printed after the Council, especially if it is a "new and revised" edition of a classic!  I try to find a PDF or book of the original, untouched version.  

Now I don't remember where I read this--it quite possibly may have been in a commentary sermon by a saint which I find in the Breviary at the Hour of Matins, but I recall it mentioning the conversion of St. Augustine and the author said that sometimes God does not grant the grace of conversion until He knows the soul is ready to follow through for the rest of their life once they are converted because after a conversion the soul becomes more culpable for their sins than before because now they know better.  This might be why the you have not seen any sign of a conversion yet.  God may be waiting for these souls to undergo certain life-changing events before giving this grace.  No one knows the mind of God, but that is certainly one reason to keep hoping even though no sign of the prayers being heard by God is being observed.  

Another thing is that God doesn't want us taking credit for any graces He gives.  If you pray for a grace and it is given, especially an important grace like a conversion, you can never, ever think that your prayers obtained that grace because you are special in any way.  All the glory MUST be given to God.  St. Augustine writes that of ourselves, we can only sin and even the desire to pray is a grace from God.  The proper attitude to have is that God in His mercy and goodness inspired you to pray for this grace and with the same mercy and goodness has granted your request.  The emphasis must be on GOD.  

If you feel you have done all you could, then so be it.  Continue along and don't give up praying.  There is nothing in your request that goes against the teaching of the Church or Scripture.  On the contrary, God commands us to pray for our neighbor and Christ Himself said that God does not want the sinner to die but to live and have life everlasting.  

Remain in humility and faith before God and continue to request this favor of Him for as long as it takes, like St. Monica did.  Leave the timing of when the grace will be given up to God.  This should give you peace of soul as you wait for what you ask of Him.  This is an act of submission to His Will, which glorifies Him and always brings interior peace while reminding us that everything depends on HIM and not on us or anything we can do of ourselves.  

You can find information on following inspirations and submission to His Will in books on abandonment to Divine Providence.  Lehody and de Caussade are great authors on this topic.  Lehody is especially good regarding inspirations. The copy I have from TAN is good.  Try to find an original version of Abandonment to Divine Providence by de Caussade online (Guttenberg?) because the one currently in print differs somewhat from the original and is not nearly as good.  I can try to send you PDFs if you can't find them but they must be for private use only and will come by We Transfer in zip format (if I can figure out how to do it!) as they are probably too large for regular email.  They are definite "basics" to have in a home library for your own spiritual life and the members of your family.    

Thanks for the compliment.  I hope what I've learned can help somebody.  They're only suggestions.

I assume your question is addressed to everyone, at least I hope it is because that's a good question and is difficult to answer.  I can tell you that if it was wrong to be around people who are less than full of grace shall we say--I should have moved away from home the day I was born lol.  

Your first obligation, from what I've read, is to protect your own soul.  If being around these people or anyone for that matter causes you to even think about sinning, avoid them.  You are responsible to God first of all for your actions, what you choose to do and not do, and your parents and relatives second.  I know this can be difficult, especially at holiday time and family reunions, etc., but you can't put yourself in a situation where you know you are weak.  This is a general rule. I'm not saying at all that you are weak or prone to temptations of this sort.  I'm just talking about things in general.  

In my own situation, I did not associate with those family members and they knew it was because I did not approve of their actions.  I got the "cold shoulder" and it hurt, but I could not be two-faced.  My avoidance of them was a constant reminder to them that they were doing wrong.  I knew there was no way I could talk them out of their actions, so I had to get the message across by avoidance.  Maybe I should have done more.  It's a tough call.  Only you know how best to deal with your own family.

One thought:  You mention your father.  If you think you will have to care for him some day when he gets old or sick, the time to discuss this with him might be NOW or else when you must care for him you will be filled with resentment and anger and all sorts of things you thought you'd never feel, especially if you're a woman.  It's hard to tell your elderly, possibly very sick father, how you felt all the years he deprived you of being a true father to you.  Best to handle this while he is younger and can handle a potentially heated discussion.  But again, only you know how he would react and if this would do any good.  

Just don't play both sides -- don't joke about it with them while you resent it inside.  Be honest with your words and actions.  Pray for prudence and know when and how to speak or not speak about it, but certainly talk to them in private (if you decide to talk about it) and don't humiliate them in front of others. Some people need to be spoken to in a matter-of-fact way or else they are ready to fight while others can't see one inch in front of them and need a good in-your-face encounter to get the message across.

As for dining out with them, certainly NO if their mistresses are there lol!  But a public place has its advantage in that perhaps a glass of wine or a beer and a good steak would put them in a more receptive mood to be spoken to AND no one likes to draw attention to themselves in a public place so they'd be less likely to loudly tell you off or argue with you or walk away from you, especially if the steak hasn't come yet!  

If you're worried about your own reputation and being seen with them, only you know best.  But face it, your dad is your dad and your grandfather is your grandfather at home or out in public.  It's the family God has given you.  As the saying goes, hate the sin but love the sinner.  The way you speak, the topics you choose to speak about, your body language all convey what type of relationship you have with them and what you think of them.  It will all come across to anyone who cares to observe you.      

My mother used to say, "Anything for peace."  That sounds good but believe me, that got our family into more trouble than you could imagine.  Very important things were not dealt with when they occurred and decades later it all came to the top and it was NOT pleasant.  I had the distinct feeling that had those family members known how other family members felt about their actions, they might have changed their ways--but it was too late.  They were dying.

Pray for guidance for yourself in this matter and conversion for them.  And all the while remember that if it weren't for the grace of God, you might be just like them.  We're capable of every sin imaginable and only God's grace prevents us from committing them all.  Thank God for letting this disgust you and continue to examine yourself and work on your own weaknesses so that you don't get the "better than thou" mentality.  At God's feet, we are all sinners.