What a miserable situation for everyone involved. I am so sorry you and your family are going through this.
Unfortunately, until your mother is able to enforce her boundary and not let him back in again, I fear this situation will continue. You cannot control your mother any more than you can control your brother. As long as there are no real consequences for his choices, why should he change?
Have you or your mother ever been to Al-Anon? It has helped a lot people make very big strides in letting go of trying to save their addicted loved ones.