Auto insurance claim denied?

A woman ran a stop sign and I hit the breaks to avoid hitting her, but the car behind me hit the rear of my car and the car behind her swerved to avoid her and hit my front. The police did not give her a ticket because 'no one was injured', and they made a lot of mistakes on the report (i.e. my license plate #, VIN #, birth dates, etc). The police report is supposed to be fixed soon. The insurance of the girl who ran the stop sign sent someone to appraise the damage, then they denied my claim saying their client wasn't at fault. The insurance of the car that rear-ended me said they are still determining fault, but if they accept it they will only fix the back end damage and not the front. What should I do? I only have liability with my insurance. Can I re-file a claim with the insurance of the girl who ran the stop sign? What's the chances they would change their minds?