Have you tried suggesting marriage counseling for you both? Tell him you will pay for it ( to make it that much easier for him to say yes to the idea). Have marriage counseling does work sometimes - it worked for me once.

Have you tried a powerful novena, such as a 54 day rosary novena?

My husband did me wrong.  I was in agony!  He went to confession 4 times and I begged him to come home.  After 5 days of being away, he came home.  Six years ago this happened.  It was a struggle because the hurt, hurts and lingers and in order to get through it, you have to talk it out ALL your thoughts a hurts and it goes on over and over.  Rejection is worse than the death of a spouse.  To prove your sorrow, will take awhile.  Trust takes a long time, it is the hardest to over come.  A priest told me to say 3 rosaries a day.  Also, thank God you have come to confession and true sorrow.  Remain as you are, no divorce.  You married for better or for worse till death do you part.  Do just that.  Never have your eyes wander any where else.  You are married and continue to stay that way.  Sign no papers.  IF your spouse is a Catholic, then your spouse must know that sins are forgiven.  Even  Mary Magdelene and St Paul and many more St. Augustine.  They had many mortal sins.  God forgave and they made heaven.  If you ever get a word in edge wise this you say to your spouse.  Also, you are fighting Satan who wants to keep you apart.  Be sure to fast, Satan hates that.  The Cure De Ars did just that and won over a villiage. You don't fast like he did, but as we do during Lent.  Our priest said a lady gave up all sweets for 2 years and her husband never drank alcohol again.  He became sick to it.  So, always give your spouse signs of your love.  Mail cards that you make yourself, and letters to your spouse and never give up.  Ask the Holy Ghost to guide you and never give up.  Even if your spouse never returns, you are an example to your children.  The whole family can learn from this grave sin and forgiveness.  We are learning, I am learning and still learning.  When the hurt hits me I go to my spouse and we cry together.  I have to discern when the devil is tempting me with the hurt and bad thoughts.  Music and TV just hits my buttons and makes me cry.  When I glance at tabloids I cry and my stomach is sick!  So, your spouse is going through all that.  When you write letters, be sure to mention the emptiness  one feels.  Never stop telling your spouse that you are so sorry and you need your spouse!  When I was in agony, I begged all of heaven and all in purgatory to pray for us and I asked God for just one very small drop of His Son's Precious Blood for the issue.  I will keep you in prayer.  It is not easy when there are so many spouses who talk with the wrong company to get ideas that everyone is doing it!  Divorce is not so bad once you do it.  It is the devil talking through them!  Age and lack of hormones and boredom and birth control contraceptives  can really get in the way.  Without contraceptives, the couples will talk their feelings out so much more and growth can happen so much more.  Be sure to look at all the angles as to why this happened.  Prayers

Please also pray to St Jude, the Patron of Desperate Cases. Best wishes.

Just don't get a divorce.

Maybe in time, they will forgive.

I am a traditional Catholic. I have had my share of crosses in this life. You do not say what you have done not that it is my business nor what your spouse has done to let you down. Again it is not my business.  However, I have been through similar situation with a friend some years ago and her husband had another woman. He behaved as if she had failed him whereas it was him who wanted out and did not want to admit to the fact he had another woman. I would go about my life if I were you, forgive him, as not forgiving him with only hurt you more than him. And live your faith. There is nothing you can do...no matter how good of a wife you are if a man has another woman that he wants. Attend Mass, receive the sacraments, say your daily Rosary. Leave him and your entire life in God's hands. Easier said than done but you are no good to yourself or your children when you are in such a state of emotional distress.  Sign no divorce papers, get a custody and support agreement in place as you owe that to yourself and your children. God bless!