How did you punish him for the stealing, removing air caps etc?
My DS1 is a similar age, and if he were doing these sorts of things, he would be grounded.
He certainly wouldn't be allowed out unaccompanied by an adult until he could prove that he could be trusted.
If he called me and my DH those names, it would be an awful long time before he got any pocket money, and he'd be doing lots of chores around the house to keep him busy.
I don't think it would be helpful to cut down the amount of time he can stay with you, as this may cause him to feel unwanted.
But he does need to have firm ground rules, and consistent punishments for bad behaviour - and those rules need to be the same at your house, at his mother's house and at school.
Does he have any interests? Maybe he could get involved with scouts or a martial arts club?
I think it would be helpful if you and your DP arranged a meeting with the school, and have your SS's mother there too.
A united front is really important.
I also think that looking into the available counselling would be beneficial. It may help him to cope better with his feelings, and help him to control his behaviour.