You can't sue a car, you can only sue a person! Although we talk about 'getting a car insured', it's actually the driver who is insured against claims for injury or damage. Your insurers could rightly point out that they've provided insurance for you and not for your passenger; in which case they'd be entitled to refuse to pay out.
Further, in general, you can only successfully sue someone for damage to property if there was either intent or negligence on their part. You've not been negligent (and there was obviously no intent), so any claim against you (or your insurers), by the aggrieved person, would be certain to fail.
Your passenger is, by virtue of her negligence, liable for the damage to the other driver's car. She can either pay up or refuse and wait to see whether the other driver pursues the matter through the small claims procedure. However, she might also take a look at her household contents policy (if she's got one). Such policies often include an element of 'third party' cover which is provided to take account of the sort of circumstances you describe.
Chris