Good for you for calling her out on the EA/OM. It was long overdue.
You did a great thing by telling her "then you do what you need to do." If you do not want a D, do NOT file. Let her do the dirty work.
You should tell her that you want the M to work and are willing to make it work but you cannot and will not tolerate a 3rd person being involved. Suggest MC. The rest will be up to her to decide what is most important for her.
As for your kids, go and see them. They are your children and you have every right as a father to go and visit with them. That house is yours too, right? I would move back in!
If you don't mind, can you elaborate on the issues between her & your mother? Why the animosity?