I too would stand my ground, not leave the house and try to make it as uncomfortable as possible for her to remain there. I would not leave the marital bedroom either.
I would continue to DB, ignore the situation as much as possible. She is living in the basement - how comfortable can that be? Can you make it more uncomfortable for her? I would put all of her clothes down there, make up, everything.
I would not participate in any family events with her. She is wayward. You are not in a happy family relationship so don't play that game with he.
You are lucky that your kids are older, I think they will be hande it better.
Continue to "play the game" who knows what can happen in 2-3 months. I would consult with a L to know your legal rights. Can you buy her out of her equity? Does she work and contribute to the family income? Are both of your names on the deed? Can you make her pay rent, utilities, etc...
