Difficult Situation

Please bear with me.
My mom is currently going thru a very tough situation. Ill try to make it as short as I can. My mom my brother and me used to live in the same house. My mom and brother bought the house under their name. My other brother has always had some animosity towards my mom. Long story short about a two weeks ago his live in girlfriend left him (but now is back with him) and at the time he had a breakdown. He blamed my mom for his girlfriend leaving him. So much so that he got extremely aggressive with my mom and essentially kicked her out of the house. I also got out of that house and for the time being my mom is staying with me. Mind you my mom did not want to leave that house cause its her house too but obviously had to leave cause she did not feel safe their with him. She left under duress. For the past year or so she had always wanted to sell the house but my brother would always say no and start yelling at her. I know people here are not lawyers but any input/suggestion of what she can do? My brother sent me a bunch of texts how she wanted her out of that house and he told me several times when his gf left him how she wanted her out of that house. When I would talk to him I could feel all the rage and anger she felt towards her. I saved all the threatening text he sent me regarding her.
She plans (with my help) getting a restraining order against him.
If she were to get a restraining order that he cant be near her and come back to her house. Will she be able to sell the house without his permission?
Sorry for the long post. Thank you.
Any input would be appreciate it.

Laws vary between states.

1st thing) I would verify who actually owns the house. That is not clear from your writing. Whose name is actually on the deed title? Because as far as the law goes, whoever is on the deed is the owner.
If it's under his name only , even if he bought with her help - then it gets hard.

2nd ) if the house is not under your mother but she helped him substantially in purchasing the house, you may consider filing a civil lawsuit. Better get a lawyer with this. It's complicated to do it on your own.

If your brother gets arrested for Domestic Violence, then its over for him. He can't live there.