I don't remember what the age requirement is to rent a golf cart but I know you must have a valid drivers license and a credit card for deposit in order to rent one. It has become very challenging to drive one these days - dodging bikes, cars, scooters, ATVs and then also know which streets run which way and which are closed on weekends. Then the added confusion on street parking - from the first to 15th of the month versus the 16th to the end (which totally confused me a few weeks ago).
You are right to be a concerned Mother. In my humble opinion, it should be you driving.