Ugh. She may have been hit by WA's STUPID "rear end" law. The law is ridiculous, awful, and despicable. It states that whomever has the REAR of their car hit (even if they were doing the hitting) is NOT at fault. People can merge into the side of you, ram you, or even Tbone you, but if your car hits the back of their car even while spinning... you're toast. So if he ran the red and she hit the back of his car in any way, she will be held at fault UNLESS you get a good lawyer. And even then, it's iffy. My neighbor was just judged to be "at fault" because a few weeks ago a car was sliding backwards in the snow and hit her parked car. No one was even in it. But because it was the BACK of the sliding car that his hers... you guessed it. She's now appealing it with legal rep.
BUT YES. Contest the ticket AND the accident. And do it with a lawyer. The lawyer part is key. And your insurance company with probably provide one (ours does, the moment we're in any kind of wreck we get THEIR teams of lawyers fighting).
I was in an accident many moons ago. It was SO obviously the other person's fault the cop wrote ME a ticket stating "Non-Negligent Driving" and outlined in handwriting what had happened just to make sure he got his 2 cents in in court if he couldn't be there that day. (For several years I had it framed in my office). The other driver ran a red light going 60 in a 30 and was also drunk at the time. All of this is documented, along with more than 20 eye witness accounts.
The other people had a lawyer and I didn't (different insurace), and at 19 I was too naieve to think I needed one, and probably didn't have the money for one (I never researched, I thought it was pretty cut and dry). I was judged to be at fault.
Whenever you're dealing with the legal system, only do it through a lawyer.