Well, the boy is indeed very naughty. But his behaviour or temperament is very likely to be caused by the environment he is livening in (ie. his family and social background).
One obvious inappropriate thing his mom has done is that the mom chooses to threaten the son when he did anything wrong. Threatening only creates fear. And fear is no good, because it will most likely make the son more rebellious. An alternative would be love and care. To have a deep talk with the son, to find out what the root cause of his rebellious reaction is and to help the son cope with the society better may be a bette method. When America has an alarmingly high psychiatric problem rate, it is clear that most of them are not caused by genetics, meaning, they can be changed for good.
Surely, the mom has tried to talk to the son. But the depth of the talk is questionable, simply because when the mom finds it urgent to have a serious conversation with the son, the son may have already developed a distrust against the mom, and the talk can be very difficult.
When the mom gives up to call the police, even the 13-year old son may yet to have a serious mental problem, he will develop one.