+1 for Cancun Valet, but the other recommendations are also good
We don't use Th Moore for airport transportation for several reasons:
they are more expensive than the others; the others use private vans which once you hit three or four people are less expensive than Th Moore's individual prices. BUT check the online sites for each one
Th Moore seems less flexible; they pick up people for the return trip earlier than needed (in my opinion).
We like being met by someone holding a sign for us (Cancun Valet, and probably USA Transfers and Canada Transfers as well?)
The service is pretty much the same on all same vans, similar drivers, etc. We just like CV.
also, even though you are technically booked for the RI, do be sure go go next door to the Royal Caribbean. More pool areas, another restaurant, the Express takeout (my favorite), etc. The 13 y/o especially may like the volleyball net set up across the pool area by the B building.