With 5 people, it'll definitely be much cheaper to rent a car to drive yourself. It cost about $50 to pick up a full size car from Avis at the Airport and drop it off at Radisson at Cape Canaveral. The return will cost about the same. Avis provides a shuttle bus between their Radisson office and the port. If you do decide on this route, I would suggest that you drop off your family and luggages at the port before returning the car to Avis at Radisson. If the shuttle bus is crowded (on occasions), it'll be much easier to find space for 1 than for 5.
We have never done it any other way. We always had the need to make grocery stops before getting on the ship. Having our own car just made that simpler.