The way you described it, the other driver hit the car door - not the car door hit the other vehicle. A judge or police officer will need to determine fault. It sounds as though the other party is "at-fault" for hitting the car door, because if she was paying attention - this accident could have been avoided.
The drivers of the vehicles need to contact the police, and let them know what happened. They will let you know their level of involvement. After that, you and your daughter will need to talk to her insurance company - so they can protect their financial responsibilities.
Many states have comparative negligence laws that may apply some fault to both parties. Negligence is the failure to exercise enough care required of a reasonable and prudent person in any given circumstance resulting in injury or damage to another person or property. If a state doesn't follow comparative negligence then they typically are based on contributory negligence; any party guilty of negligence, to any degree, was unable to achieve recovery from the other party.
The concept of comparative negligence is to allow damage recovery reduced by a person’s own percentage of negligence. In order to have a clear understanding of how comparative negligence works, it’s necessary to contrast it with contributory negligence.