If you and your daughter were not injured and you have comprehensive coverage on your automobile, work with your insurance company to have your car fixed. They will go after the adverse driver's company if they feel it has merit. If either of you were hurt or you have no comprehensive coverage, hire an attorney to represent your interest.
This response does not create a lawyer client relationship. Each case is determined on its specific facts and this reply is intended for a general audience and facts particular to your case may affect the answer. Consult with an attorney in person for specific answers to your questions.
First the named insured on a policy may well be different then the driver involved - not unusual. Their carrier is alleging what is called a reverse rearender - very hard to prove. You will need to let this rest in the hands of your insurance. If you are unhappy with the way the adjuster is proceeding contact their manager. The problem with your daughter is that she is not truly independent - but better then nothing.
Most important, communicate with your insurance company in writing and note every employee and extension number you speak with by phone. That's why you have insurance. Cooperate fully with any attorney the insurance company assigned to your case. Insist in writing that the facts are wrong.
If this produces no results, use the Find a Lawyer function at the bottom of this page for a very good Avvo attorney in your area.
The above is general legal and business analysis. It is not "legal advice" but analysis, and different lawyers may analyse this matter differently, especially if there are additional facts not reflected in the question. I am not your attorney until retained by a written retainer agreement signed by both of us. I am only licensed in California. See also avvo.com terms and conditions item 9, incorporated as if it was reprinted here.
The fact of the matter is that insurance companies are not always as helpful as they should be. In accordance with Mr. Doland's answer, be persistent and document who you talk with. Your insurance company has a legal obligation to represent you and look out for your best interest. Best of luck.