I'd repair it prior to trade-in and they will inspect it prior to finalizing the trade. As long as the repairs meet their standards for trade-in, you're good.
I assume you have full coverage, right? If so, file a claim w/your own insurance via subrogation. This is why you pay for comprehensive so use it.
This will be the fastest track to getting your car right again before the trade-in. Your rates won't be affected and your insurance will work with the other driver and their insurance to get reimbursed. You use your own repair shop(s) for estimates and repairs and aren't subject to the other driver's insurance crappy requirements, if there are any.
Your insurance has the most motivation to make sure you're happy so go this route. Going this route will make the best of a crappy situation that you didn't ask for.