I was picked on A LOT as a child. In my experience, kids who are bullies have parents who are assholes. Even if you had video evidence, this woman probably won't do anything because she's already led her child to believe that he's entitled to pick on other kids for some reason.
Next time this little shit does something, call the cops. Get a restraining order if you have to. You won't be able to reason with her because she's the reason her kid is a bully.