I'm a newbie but after reading your post I thought I’d share some of my experience as the unfaithful partner in a relationship for whatever it might be worth in your situation.
First I’d seek out the counseling services of DB before you do anything major. It’s invaluable.
I’d be cautious about confronting the other man. Based on my experience it could have brought me and the other person closer together rather than apart.
The real thing I wanted to share with you is the idea that the experience of having an affair is very much like having an addition. It’s not necessarily the other person, but the experience itself that is very addictive.
I would you encourage you to interact with your wife as if she was an addict. I’m not necessarily talking about compassion. What I think I mean is that you can’t control the addict’s choices, you can only control your own. So you are entitled to control your own wellbeing and those of your kids . Also you are entitled not to give support to the person in pursuit of their addiction i.e. give money, give support, housing, etc.
Most addicts won’t make the choice to quit until they come face to cost of their addiction; financial cost, lost relationships, dislocation, etc.. Therefore doing things that make her face the results of her choices may be the ONLY thing that works: No longer providing financial support, no longer providing emotional support that the OTHER cannot provide, separate living arrangements for you and the kids.
All with the message of “I love you; if you want to make things better I am here to work with you; but I am not willing to do anything that supports the choices you are making in this regard”
