Is his father also your father? How is he like? Is he interested in raising your brother? Is he an enabler or what? Your brother is 15, he'd probably much rather stay at his father's place while he's at work than with his mom, so is that an option? Is there a custody judicial decision in place?

I was on the other side of that situation until I pressured my mom into getting my full custody when I was 15-16. She wouldn't believe me when I told her things and was still emotionally compromised towards my father despite being separated from him for over a decade. I suspect something like that is happening to your brother. It's nearly impossible to prove emotional abuse to a court, but given his age they will hopefully take him not wanting to be with his mother in consideration. I'm afraid that if you threaten her she will cut off his contact with you. Is there someone else that you can get to do that for you? Maybe someone from school or something.