The house was tainted. Let her have it and the debt that goes with it.
You'll soon be in a position one day to own your own home again. Maybe it will be a condo or townhouse or duplex or tiny little ranch. Whatever.
But it will be a clean start and the house will be yours and yours alone, untouched by so-called women who have no morals whatsoever and rut like pigs with anyone who'll have them. No loss there.