There has to be something that you could do that affects her. Do you give her any financial assistance for her car, car expenses, phone, beautician, manicures, cosmetics, gym fees, trips, etc.?
I forget, if you mentioned, the sleeping arrangements when she's home. Is she sleeping in your bedroom? If so, where do you sleep?
Are you telling her you have plans for the weekend and she'll have to stay with the kids? Would she take them to OM's?
Are you washing her clothes, cleaning her messes, cooking her meals, running her errands, etc.?
I am going to say this very bluntly. The only reason she is even tolerating you as little as she does, is b/c your services benefits her. You do the housework, cook, take care of the kids, and financially support the family. But mainly, you are her backup plan. When the A is over, there you will be.......waiting for her to return. Meanwhile, she is free to do whatever the blazes she wants. Why on earth would she be thinking of coming home? She comes home to eat and get clean clothes. While she's there, she kisses the kids goodnight, and she's on her merry way. What can you do to put a cramp in her lifestyle?
Maybe you are the kind of man that waits it out. You sound as if that is what you're doing, and then you want to put it behind you and move on. Listen, even if the A plays out, and even if she came home, what would she feel for you? Do you want me to answer that question?
The woman has no respect for you. She is not concerned about your feelings or what you think of her. She is rubbing this wayward lifestyle in your face, while you keep the home fires burning. If you proclaim what you won't put up with from her, she laughs behind your back. She feels no remorse for her actions. If she came home today and said the A is over, she would have zero feelings for you. She has to respect you and she has to feel attraction before she feels in love with you.
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!