SO wants to break up our new family

Hey all, I'm just writing this to vent, because I feel completely lost and very lonely.

My bf and I are fighting alot since our son is born. He quit his job and is now studying at home (career change) and I'm still home because I took a lot of vacation days. So we are in eachothers face a lot. We had a huge fight this morning, things got out of hand immensely.

His mom had an accident a few years ago,in which she ended up with braindamage. She functiones at the level of a child. And can get very angry out of nowhere. She also had paralized arms, which she can now use again but has little strength in.

The fight was about my bf wanting his mom to watch our five month old son when he had to study and I would be at work. I don't want her to for obvious reasons, so I told him that. He insisted upon us trying. I said there was no point because I'd not support it. He got upset and called me a bitch. Told me to piss off. I told him I wouldn't and that I was fed up with him calling me names, which happens frequently. He told me I had brain damage myself and touched my forehead with his indexfinger repeatedly, like knocking. I pushed him away and said dont touch me. He pushed me. Etc. It was ugly. Nobody got hurt but it wasn't okay from both sides.

After that, he said he was done and wanted to end the relationship. We just bought a house last August and have a baby together.

This relationship is toxic. But I do want to work on stuff with him for our son. He doesn't.

He gave me two choices from which to pick in a weeks time: sell the house and 50/50 have our son, or co parent in this house. Option two included our cats staying in the shed outside overnight and his mom babysitting our kid. If I don't pick, he does.

What the hell should I do?

Edit: we bought our house at a terrible time, if we sell now we're both in significant debt. I want to work things out with him for our son, I dont want him to go through having 2 homes and not having an intact family.