Obviously the kid lives with his g-mother if his mother isn't at home, and from experience, a parent who's a shitty parent doesn't do something as drastic as calling the police on her child because it's a difficult decision to make to teach them a lesson. Also, I SERIOUSLY doubt that the mother is teaching her son to go around punching cops, ESPECIALLY since she called the cops to take him away.
You wanna hear how it really went? The kid is a problem child, the mother has tried everything to reign in her kid and nothing is working; he's just getting worse. He punches a cop, shoplifts from a store, and shows absolutely no regard for his mother or grandmother. They are at the end of their wits, so they try to teach him a lesson. It's not like he's going to prison or anything...they let him out an hour later. It was just to teach him a lesson and maybe try to knock some sense into him. There are shitty parents, but just because some kid IS A LITTLE SHIT doesn't mean he/she has shitty parents.