You've gotten excellent advice here.
I don't usually handle auto claims, but I do have a basic understanding of auto claims here in New York -- I see that's where the OP is from as well.
OP, I'm not sure who owned the car -- the mother or the daughter. If the mother owns the car and the daughter was driving it with moher's permission, both mother and daughter can be held responsible for any damages as a result of the accident. If the daughter owned the car, there are some very clever plaitniffs' lawyers who will find a way to bring the mother into the suit, assuming there's a need to do so -- e.g., the policy limits on the daughter's insurance are not sufficient to pay the damages. the fact that the daughter is 17 does not prevent a claim from being made against her, but the fact that she's 17 makes it likely a plaintiff's lawyer will seek to bring in the parents -- and their insurance -- if he's got a serious bodily injury claim.
auto liability insurance has two components. the policy indemnifies you if you have to pay damages -- and that includes both property damages and bodily injury claims. bare-bones coverage in NY is $25,000 per person/$50,000 per accident.
and the policy provides that the insurance company will defend the insured with respect to any claim seeking those damages. the company will investigate the claim and hire a lawyer if necessary to defend against a claim or suit.
in NY property damage claims and bodily injury claims are handled differently. if your car is damaged in an accident you can either have your own insurance company fix it -- and they will make a claim against the other driver on your behlaf -- or you can deal directly with the insurance company for the other driver.
bodily injury claims, on the other hand...well, no-fault coverage is mandatory in NY. you're supposed to use your own policy's no-fault benefits first, and only if you have a serious injury are you allowed to sue the driver of the other car. the auto insurer's claims department will know how to deal with this.