As Zig says, it's not your business.
What you need to do is file for divorce (if you haven't already done so) and ask the court for exclusive residence of the home.
However, if that happens, you will almost certainly be ordered to pay all of the costs. You will need to find some way to afford it - either renting out a room, taking a second job, or whatever it takes. You can also ask for temporary child support and/or alimony (if appropriate), at the same time.
Alternatively, you can let him continue to pay 1/2 of the mortgage and let him use the house sometimes. How he deals with his ex is his problem. However, if his ex is unwilling to allow the kid there when you're there, and Dad decides not to pay his half of the mortgage because of it, you might end up losing by insisting on staying there. An alternative would be for Dad to continue to pay half the mortgage and get to use the house for his visitation. You get the house the rest of the time - and stay with friends or family (or even a cheap hotel) when Dad is visiting his kid.
In the end, though, you're probably going to have to sell the house, so the more you can get it fixed up before the divorce is final, the better.