You said you wanted to switch him to the public defender. The taxpayers pay for the public defender.
That's the way I read it at first, too. However, to be fair, if you read the rest of the posts, OP seems to be asking if they can switch to a public defender - even if they still have to pay.
I'm not sure that makes any sense, though. Why would you want an overworked public defender if you have to pay, anyway?
By the way, I was on a jury for a public defender trial. The lawyer was just incompetent.
I get the sense that OP doesn't really care. She has reached the end of her rope and seems to have decided that jail time might be what it takes to straighten the kid out.
Of course, that messes up the rest of his life, as well. If it were me, I'd be looking at getting him a decent lawyer and stipulate that he'll be going to military school where they can pound some discipline into him.
But I haven't been where OP is, so take that with a grain of salt.