I have to assume things work differently in the US?
In the UK if you're rear ended its pretty much an open and shut case, wthi liability falling on the other party. The other party's insurer would have to pay for all repairs and any other inconvenience (rental car, until yours can be repaired).
I can only assume the 30 day limit is with your insurer and they aren't expecting to recoup the costs from the other insurer before then. Therefore you have to pay for the remaining rental period yourself, subsequently claiming it from the other parties insurer. If that's e case I'd kick up a fuss with your insurer and ask them to put pressure on the other parties insurer to cough up for the rental portion of the claim quickly, or find a way to get the parts for your car.