For minor property damage situations like this, generally I'd advise people to run it through their insurance, and let it handle getting everything back from the at fault carrier. Lawyers don't take property only cases usually. And even if they did, the typical contingent fee for a lawyer would leave you worse off than had you just taken whatever was offered (because there usually isn't much room to pump up the number in negotiations on a property damage only case, the disputed amount is usually pretty small). Another option for higher value property cases is hiring a public adjuster (their fees are typically much lower than an attorneys).
A TDI complaint isn't going to go anywhere when you're talking about a 3rd party insurer. They technically don't have any obligation to the other driver, only their insured.
A lawsuit (smalls claims or otherwise) is really the only other recourse. But, again, really not worth the time you'd spend doing it for a case like this. If your own insurance is an option in these situations, that is your best bet.