There is a process in place to have your mentally ill brother declared legally deficient and strip him of his gun rights if he has demonstrated that he is a danger to himself or others.

Has your brother actually demonstrated that he is a danger? If so then you should follow the process the law sets out for dealing with it.

And I'm glad we both agree that black markets can't be eliminated. That establishes that a broad ban on guns will mean that only criminals can get them. That doesn't sound like an improvement to me as criminals are the ones we would actually want to stop from owning guns, not law abiding citizens.