WTBH,
You will have to check with your attorney but when I divorced the decree specified who got what and the bank had to comply, we did not have to refinance, also the attorney should be able to look at the child support formula for your state and tell you approximately what you will be recieving if you get sole custody, you may be able to stay in the house.
Depending on how things work with the prosecutor, they may put him on suspended sentence, which would be excellent incentive for him to behave, which could include terms about staying away from you, keeping a job, paying child support on time, etc.
I gues what I am saying is don't juimp to fast and burn your credit, you have lots of balls in the air which your lawyer and the courts can help you manage.
Big hugs and best of luck,
Bill