Tesla's right. I'm going through this right now, but luckily, my name is on the deed and mortgage so "our" house is thought of as marital property.
I'm sad for your situation, Sweetness, it's not easy. Perv returned briefly for ten days and it was intolerable living with him after Dday. I never knew if the next thing I did or said would send him packing, for it felt like every time I spoke, he was getting his toothbrush and backpack. It was really awful. Then after one night time sneak out, DD and I didn't know if he would be here in the morning when we woke up.
I'm glad you don't need the house and what I'm learning and have been advised is that anything I can let go of will help the horrible process go by faster.
Child support (CS on here) is frequently given to the parent with physical custody-in our state-and is based on a percent of salary.
The custody part was hard for me to understand but I finally get it better. There are different kinds and L described some of it -"joint"-as sharing information and Perv getting to have a say in some of DD's upbringing.
"Physical custody" was more important for me, for that's where or with whom a child would actually live.
It's really up to you to stay or go and if you know you won't have a chance at the house, in some ways I think, rip that band aid off! I've had to do that with some other aspects and it emotionally ruined me to do, but I'm on the other side of some things now because of it.
Maybe making a list of ideas about living where you do and what a new place would bring? Maybe actually going to see some alternatives and letting yourself think about having different walls there when you wake up in the morning...opening these thought channels sometimes has helped me be less scared and able to take back a tiny bit of control that got taken away.
Sorry for my long post, for I live that very thing.
A person is a person, no matter how small. -Dr. Suess
Perserverance and spirit have done wonders in all ages.