Firstly, I’m sorry you are having to deal with this, especially with everything going on this year.
I don’t have any experience in this, but I will say this, it was her choice to end the relationship, she is the one who cheated, it should be her leaving the home.
From the sounds of it. The house is equally yours and hers? That’s the hard bit, I would suggest standing your ground, but remaining as polite as possible. She has already taken your marriage from you, now she wants to take your home from you? Thats not right.