I'd send them to school during the week (the childhood equivalent of work) rather than make them stay in their rooms (the childhood equivalent of prison) 7 days a week. If you consider work (or school) 'doing whatever they want' you must have a lot softer job than most folks.
...and if there are none, then sure - foster care
So you do want to put it back on the taxpayers.
Rather than give a CRIMINAL a break, yes.
Criminals are people who BREAK THE LAW. They do not repeatedly DESERVE breaks.
Do you remember "Don't the crime, if you can't serve the time?"
I'm not the criminal here, this idiot is. He's repeatedly shown contempt for the police, and general civility laws that help keep good order.
Children, or not, he should be reprimanded appropriately. I have ZERO compassion for an idiot who sees the police lights in their mirror and they hit the gas pedal, thinking they can run away. You might get away from the cop behind you, but his buddies on the radio? Probably not.