You simply need to see a lawyer.

I really don’t understand why all this moving in and out and buying and selling happens in the absence of legal separation agreement or legal advice etc By legal advice I don’t mean talk with a friend who is lawyer. Not the same.

I understand it’s expensive. But try to find free consultation or discount services. Divorce is expensive. But so is supporting other people who apparently can hold a job and who are nasty to you.

Yes she is within her rights to move back in as it’s her house too. See a lawyer. What you need is legal consultation.