So in an hour or so I face her mother. I'm scared. Really fucking scared
She has insurance just for these exact reasons, like anyone else.
Yes, it sucks to have an accident. But you didn't get any tickets because it wasn't your fault. The police report will be what their insurance company works with to determine fault. The old lady's insurance should pay to fix your girlfriend's car.
The mother probably will feel least bad if you say that you're very sorry, that you weren't speeding, were wearing your seatbelt, were very cautious of the particular intersection because you're aware it's a bad one, but still there was nothing you could do to avoid it since the woman advanced past her stop sign prematurely (maybe she ran it, maybe she didn't, who knows).
A basic fact of life is that shit happens. Make it obvious that you did everything you could to avoid said shit from happening and the rest will fall into place when the police report gets into her hands.
If you have a copy, bring it. If you don't, maybe you have time to pick one up from the police station.
You'll be fine! You were very nearly broadsided in the driver's side door while YOU were the driver. That could've been a VERY bad situation, but thank God you're completely unharmed and the car has a smashed area that her insurance will pay for. That is a blessing. You're to be congratulated on your fine recovery skills... you clearly handled the car well despite being run into, because you're not telling us you spun the thing around or anything. And you weren't drunk, you didn't run from the police....
it's all as good as it can be, considering. Yes it's an accident, but it wasn't your fault and there is no extra teenage BS to go along with it. That's as much as the woman can ask for.