having just gone through your situation, I would consider getting a lawyer.
I know it sounds over the top, but no one is really on your side at this point.

Your car’s accident history just went up by 1, even if your insurance doesn’t up your premium for an accident that wasn’t your fault, it still goes on the record that you were in an accident, and realistically, you’re very unlikely to get paid the full cost to restore the car to pre accident condition. Insurance will refuse to pay for anything new, because the car was not new, so you’re either going to pay the difference for a new part/new paint or settle for some form of repair/replacement that leaves the car in less than pre-accident condition. It sucks to think that anyone can just plow into your car and the best you can hope to get is a car that is worth less and with damage that is mostly, but not completely repaired.

What difference will a lawyer make? I that route yet, but I remember a google search showing than average traffic accident settlements were something like $15k plus in the US.

I don’t need 10k+ for a rear ended bumper, but based on those payouts, it seems plausible that a lawyer could get you enough to fully repair the car, be compensated for the drop in the car’s value with enough left to pay the lawyers fee.

And heres one more thought for you. Could that person who hit your daughter’s car turn around and sue you for damages?

My parents were stopped at an intersection when a guy riding a scooter in flip flops and no helmet, slammed into the back of their car.

There was no question of fault, but that guy was uninsured, had major medical bills from the accident, wouldn’t be able to work for months and had a family feed. Some ambulance chaser convinced them that he could get them a bunch of money and that’s exactly what happened. They filed a suit and got a 30/40k settlement. People are crazy!