It sounds like you have two issues.

One is whether your marriage is valid or not which could be answered by a Traditional priest. The NO priest will say yes it is valid.

Two, is where to get counseling and if it would be yourself or both you and your wife together.
It may be near impossible to find a Traditional Catholic counselor but a counselor that does strictly communication techniques is most likely to not give any heretical suggestions.  imo.
As far as I know insurance will not pay for counseling that is openly giving religously based therapy/advice.

There could be non-professional counselors for that reason in your Traditional parish so it would not hurt to ask the priest.

ihth

Prayers..

Do not discount the abilities of all non-religious counselors. Some of them can still help. There are some good eggs out there.

I would suggest it, perhaps for you alone at first. One way or another you should be able to find a referral to an inexpensive counselor.

A counselor doesn't have to agree with all you believe to help heal breaches between people, and help a person achieve his goals.

Fr. Chad Ripperger, F.S.S.P., has written some books on psychology and founding it in Catholic spirituality. And some of his audio sermons online cover marriage issues and the different ways men and women think. I've found them quite helpful.

I don't know what your issues are.. but you've cited a lot of problems with your wife's beliefs.. and certainly, they are true problems.. but give an impression of someone who, forgive me, I may be wrong.. might be a bit too tense and focused on the externals.. but a person who works on himself primarily and how he relates, in a peaceful, and graceful way, I think will make the best progress. A father is the chief provider of grace and spiritual protection for a family through his prayers for them.

If you become who you should be.. and let things flow naturally from the good person you've the more become.. you may make progress better than if you've (I have no idea if you have) been trying to force things with authority she does not yet acknowledge.

People are slow to change, some things can be too much at once for their comfort level. Small changes step by step..

Forgive my advice I pray, if it is useless.

Generally things meant for the more personal forum aren't to be in detail discussed over the Internet, but in person with someone who can help and respect privacy.

St. Joseph is a good saint to turn to. We persuade people with grace and love, rather than force, and all things have their time and season.

St. Benedict medals, properly blessed, are helpful for spiritual warfare. A whole bunch of them. Four, buried at the four corners of the house are useful for spiritual protection. If one is being spiritually troubled in the mind, touch one to the forehead while praying.

When first acquired, note however, there can be an antagonistic reaction from the threatened enemy. One should pray to mitigate this, prayers such as the St. Michael prayer.

Hope this all is not entirely useless and off base, perhaps a little will provide food for thought.

I think there is a great and urgent need for professional counselors and psychologists in traditional Catholic communities, who receive the necessary training at the schools and Universities whilst cultivating an interior life of prayer and the reception of the Sacraments, together with the practice of the virtues, that will enable them to discern that which is false in the modern day pedagogical modules and constructs wherewith they would be trained and educated at said institutions and hold on to that which is useful and necessary for these fields.

Many people often think that a Priest knows everything, and that he has the competence to answer any question or solve any problem. However, a man does not go to the Seminary to become a scientist, or a psychologist, or a medical physician, or even a theologian. He goes to the Seminary to become a Priest, a Pastor of souls, and he learns the rudimentary things about the many branches of the sacred sciences necessary for the worthy and decorous performance of the duties and necessities of his Priestly state. A Priest cannot really replace a professional counselor or a psychologist in most instances.

Lanciano, as TKGS has wisely written, we cannot satisfactorily and accurately answer the queries you have as we are not acquainted with the details of your predicament. All that we can do is point out some things that may prove useful.

From what I have read in your post, I can see (unless I am mistaken) that there are two fundamental issues that are essentially independent but are quite intertwined in the practical order of things: 1) one's personal search for the profession and practice of the traditional Catholic faith; and 2) the problematic ramifications that such a search tends to have on the domestic order of one's household, and this is especially complex when one happens to be the head of the household as husband and father, with the care of a wife and children such a one must bear.

For the first issue, the counsel of your Father Confessor and Spiritual director must be sought, together with studious and prayerful reading. For the latter issue, the help of a counselor would be needed, depending upon the variable factors in any given individual predicament. Of course, prayer is the first and best recourse for both issues.

The problematic issues that affect one's household when one ventures forth in search of the true Catholic faith are things that many here have probably experienced in some way or another. Perhaps if people would relate their experiences, you can get some ideas as to how to deal with this situation.

I have known several men who are in a similar situation which you describe, some of whom have been abandoned by their wives and have bereft them of their children. They ascribe their ability to cope with such a disastrous predicament to the counsel of their Spiritual Directors, the frequent reception of the Sacraments and a life of prayer that will enable one to see things differently and attain to a sort of discretion that will allow one to know the best way to approach problems in communication.

I wish I could be of substantial assistance, but I will keep you in my prayers.