What are my rights on rental reimbursement from the other party?

In NY State, another car hit mine while it was parked. They left a note, and the insurance claim is going through. However, I had to get a rental while my vehicle was getting repaired. The repairs took longer than expected, and as a result, the other person's insurance company is refusing to pay for the whole thing. They claim they only pay the industry standard. However, had the other person not hit my car, I wouldn't have had to pay a penny, so I don't see how they are *not* responsible for the whole thing. So I'm looking at taking the other driver to small claims court. His insurance company has stated that they will vigorously defend any attempt to get more money. Do I have a case? Or is their argument likely to prevail?