I'm not a lawyer!
This is what I would do in your situation and why.
1: Contact your insurance company and explain the situation. Let them cover it. The reason behind this is that the mother of the kid who hit your car may decide not to pay the body shop and then they would expect you to make payment. Read this forum, there are sob stories all over it about uninsured drivers doing damage, promising to pay for it and then not following through.
2: Involve the police. The kid needs to learn a lesson. Yeah, it would make you the "bad" guy/gal but, tough crap! You have to protect your interests as best you can. If you later wind up having to drag the kid and his mom into court, they will almost certainly have a sob story for the judge including how they can't afford to pay you but $10.00 per month until the debt is paid.
3: If they can afford to pay you for what is likely several thousand dollars in damage to your vehicle then why in the hell don't they have insurance on the car and/or driver? See where I'm going with this?
4: Don't use "their" body shop! It is likely a friend of theirs doing them a favor. How likely is that friend to fix your car right when he almost assuredly knows that payment from the other party might be months in coming? How likely is he to do the repair in a timely manner? What if he does a shoddy job and you have to take it back for warranty work? Will he use aftermarket (read: not guaranteed to fit right) parts in order to save his friends some money?
I sincerely hope I'm wrong about all of the above but it has been proven time and time again that doing strangers such a huge favor usually comes back to bite the victims of their idiocy in the butt.
I wish you the best of luck in this!
