I like your attitude! Same as mine. I am definitely staying with the house and most likely will get 50~50 with my kids. If she pushes it, she will most likely lose and possibly risk not getting what I am fairly proposing to her.
My W left the house already and that is one big strike against her. Stay with the house. You may lose, but dont give in as once you leave the house it lessens your leaverage for shared custody.