I dont understand how you can conclude the insurance isnt a minimum level policy, at least regarding property damage and personal injury liability. They would have to have collision on the policy but that doesnt mean they couldnt leave the other items at the minimum required by law.
Has the other insurance offered to pay the property damage claim in full?
in New York pip also includes lost wages and the per diem I spoke of as part of the mandatory minimum pip insurance.
its not cheap to hire an attorney so you may want to crunch the numbers to see if there is a chance at gaining if you sue.
btw: her losses regarding her car is the fair market value of the car at the time of the accident along with the possibility of some minor incidentals. What she paid for a down payment or that she had to come up with another down payment is meaningless to the calculation.

