I tried this one time. I talked to someone about this and they told me that if the person was not married and had no kids that the parent could put them in treatment. The parent would be the next of kin but if they had kids or a spouse it would be up to them. I talked to an ER doctor about this and that what he told me.
But....that person will have to prove that they are a risk to themselves and the person that is trying to get them help. He would have to be to the point of suicide or hurting your mom. If your mom is scared of him or if he has tried to hurt her then she can. I had called a rehab center and asked this question. They adviced me to call a mental health center and see what they said. If he gets violet or starts screaming at her she needs to get someone even if it is the cops that can see it too because he is prob gonna say she is just saying these things and he wasnt doing it. She calls the cops on him they can make him leave if they see he is a danger to her. It might not be something she wants to do to her son but it might get him some help.
It would prob be hard for you to get him out of your moms house with out a fight. Mom is just gonna have to take it in her own hands and lay the law down to him. He should have more respect for her than this she is giving him a roof over his head.
If she has a mental health office close by call them and see what they tell you. I hope your mom is ok and stays safe.
Let me know what happens. I will be praying for you and your family.