In your narrative I see anger, fear, lack of trust.
If you're smart -- and I suspect that you are -- you will get a marriage counselor for yourself. At the present, the #1 problem is YOU and what YOU are going to do with your situation.
Chances are you'll need to work on abuse/neglect issues from your own childhood (it's a standard thing, because hardly any parents ever know what they're doing, so don't worry about it). So that'll be a lot of sessions between you and your counselor to work on you.
Then, you'll have to work on issues dealing with the relationship between you and your wife. Talk with your counselor to see what would be the best way to do that.
Your wife will probably need a counselor to help her work through whatever it is that she feels the need to work through. Whatever you do, don't tell her that she has to get a counselor. The moment you put your guiding hand to her counseling, you've lost a lot of "Brownie Points." Just make the resources for rehabilitating your relationship available, and let her take the initiative to work on her own issues.
Counselors are not cheap, but I guarantee you (triple your money back!!!) whatever you spend in counseling sessions will be a small fraction of what you could pay to divorce lawyers, and for counseling for your children. Yep, your dysfunctional marital relationship is currently affecting your kids. They are learning from you how married couples get along. If they feel insecure now because of your stormy relationship, they will carry those emotions with them into adolescense and into adulthood, and will conduct their relationships the same way you do.
However . . . you could give your kids a priceless gift -- You can show them how to heal a damaged marriage relationship. They had front row seats to its fall, they will have front row seats to its healing. That's the sort of lesson that not too many children get a chance to learn, so if anything is good about this situation, this is it.
The best thing you can give your wife right now to reassure her of a better future is Forgiveness. You shouldn't tell her that you forgive her; you should forgive her. Understand that her other relationship grew out of problems with your own, and nursing resentment will lead to blame and anger, which will make resolution of your problems impossible. So, Forgive.
Enough of this . . . Go find yourself a counselor.