Sorry to hear that you're maybe separating, ending a marriage always sucks no matter what. I watched my brother go through a bad divorce, and he was worried about that too as a stay at home dad. the courts made her pay spousal support though so he was okay, also there is welfare. The most important thing is your happiness! I found this resource which could be helpful about bills. https://blog.thistoo.co/blog/2016/6/10/bills-after-divorce good luck with everything. To me, it sounds like you need to divorce.
One thing you need to know is that unless your spouse can prove that he contributed to the house he may have no claim to it (since it was a gift from your dad). In which case you don't need to move. You may be surprised at what he may wind up paying you in child support (if you have kids) and alimony (depending on how long you have been married). Years before my divorce I figured out I could make it on my own (would have had to cut back on some things, really did I need to pay for cable TV.)