What should I do about my abusive brother?

Ay, no! My brother wants to move to this school really far away from our house(~ten miles). Our designated school is just around the corner (½ mile). He wants to change school because he doesn’t have any friends at the school he’s currently attending. Which I think is a big lie because I constantly see him with his peeps. He’s been threatening my mom about if she doesn’t change him schools, he’ll not only talk back to her and tell her shit ,but also, hit her. Tonight as he was being an annoying asshole playing around and throwing items in the kitchen, my mom got up and told him to stop it. He kept going. She then heard a “crack” and started to pick up the item. Not only was he talking shit to her at that moment, he also pushed her! HARD! Fortunately, she found her balance and did not fall. I was about to get up and start beating the hell out of him, but then, I wanted to see how my mom reacted. SHE didn’t do anything! WTF! I mean, if I was her, I would’ve been kicking his ass and getting him the fuck out of the house! But she didn’t. I constantly tell her to just kick him out, but she won’t listen. What should I do? Any advice?