Is there any of her family who can take care of her? What would she do if you were not there? Maybe OM would like to take care of her.
When a WAW in an A is as rebellious as yours is being, you've got to take tough messures. Are you familiar with the term Dropping the Rope? I believe you've got to drop her if your M ever stands a chance. If she believes you don't want her and are happy without her, that may get her attention. But, here's the problem.....she is deeply addicted to having an A and I don't think she is going to cut that off easily. She will need to want you very badly and have to work her butt off to get you.
No more being passive! Take steps to protect yourself financially and get your kids. Pack her bags and send her on her way. You keep the home and let her support herself, pay for her own car, insurance, room & board,etc.
If that don't take the fun out of cheating, nothing will.
If you don't want to do that b/c she's sick, why not give her a couple weeks notice....maybe she'll put pressure on OM and then see for herself if he tries to backpeddle. Let her see if "he" is willing to support her.
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!