Why do you need to rent a car? That is one of the things we love about cruising. My DH gets to enjoy everything too. We don't worry about getting lost and wasting time at a rental agency. If you are doing a pre or post stay at the port, get a hotel with a shuttle. On islands or at ports, take a taxi tour. It will definetly be cheaper. Exception would be a tour to Tulum or Sting Ray City on Grand Cayman book Capt. Marvin.
p.s. My daughter has the same name but spelt with a C.