Does his mother know of this situation with him? How disrespectful he is, etc? Have you consulted a lawyer? I would suggest that first.
I don't really understand this. It's not as if he has a separate apartment on your property. I don't understand why you can't just put his stuff in a storage unit and change the locks. This is a family matter not a tenant/landlord issue.
I'm sure his mother doesn't want him in her house which is why she is happy to pay his rent. But if she is on your side, why not get her more involved. She can stop paying the rent or she can pay the storage unit fee for him. Once he's out physically and the locks are changed, if he was to call the cops on you, what's to stop you from saying, "No officer, he never lived here, I don't know what he's talking about."
He sounds like he needs medication. Maybe his brother can get him to the doctor.
I'm sorry for your troubles. You can vent here anytime.