I went through this a few months back, but the driver also had no license and the insurance card he showed the cops was fraudulent. I was lucky. As part of an unisured motorists claim investigation my insurance company found a valid policy on the other vehicle. I was able to file a claim directly with the other company and paid nothing out of pocket.
If you have full coverage or unisured motorist just file the claim with your own insurance company. You can then sue the other party in small claims court for your deductible. Since you are insured, I doubt you will be able to sue for the total cost of repairs, only what you pay out of pocket. Your local laws may differ, so it would be wise to check it out. If he's from out of state I wouldn't hold my breath for him to show up to court anyway.
You can also go to the kid and his father and tell him to pony up your $500 deductible (you deserve a little something for your trouble) and maybe he'll do the right thing. I wouldn't count on it, though. The kind of person who drives around without liability insurance usually knows very little about doing the right thing.
I understand how you feel. I too was furious. Your wife is probably right, though. You may just end up taking a $250 bite out of an excrement sandwich. It sucks that some people don't take responsibility for their actions, but that attitude seems to be running rampant these days.
BRW, the cop let the guy who hit me go free as well. I would have expected some kind of arrest for driving without a license, but apparently not. The cop just drove away, leaving the unlicensed driver to get right back into the car and drive away. I don't get it.
Good luck, and try to look on the bright side. No one got hurt and that's what is truly important.