""This past week me and my father flew down to Arizona state. We rented a car there, and the women at the desk mentioned that we should purchase some insurance from them, just incase we were to get in an accident, because (According to her) Arizona state law prohibited our insurance from paying and that if we did not have their coverage, that we would have to pay every day that the car was out of service, until it was able to be used again. Is this a true law, or could we have just not taken the insurance from them, and been okay with the one we already had? I dun know if that makes sense. If not tell me. Ill try and write it another way.""
It would depend on what coverage you father had on his own vehicle as far as if it would cover the rental car or not.
""that we would have to pay every day that the car was out of service, until it was able to be used again.""
Once your dad returned the car, whatever insurance he had during the contract would not extend beyond that. So if she was saying once he turned it in he would have to continue to pay for the car until it was rented again would be a false statement. But unless this was in writing there would be no way of proving she said that. Does he still have the car? If so contact his insurance company and if the car is covered, go to the car rental place and cancel the additional insurance. I don't believe that he can get a retroactive refund though.