You obviously have a WAW who has had several EA's, that you know about. Unless she gets professional therapy, she may continue to bounce from one man to the next. She's looking for somebody to make her feel good, and she gets it from new R's.
You may have to get a Judge to help you get your kids, but you to need physical custody, especially since there are men coming and going out of that house. Do you have a lawyer?
I know you must be in terrible pain over everything she's done. Your main priority is getting the children into a safe envirnoment. Do that first, then focus on getting your life straightened out.
It is not about what you feel should work in your M. It is about doing the work that gets the right results. Do what works!