I agree the Rosewood Mayakoba would be the easiest to get to (UA has many flights to Cancun). It’s a fabulous, super child friendly hotel.
Rosewood Mayakoba - Riviera Maya, Mexico

UA can get you to the equally wonderful FS in Costa Rica. But this one might be better saved for when your child is a little older and can appreciate all the animals.
TRIP REPORT: The Peace Lodge & Four Seasons Peninsula Papagayo (Costa Rica)

Both have plunge pools available in the rooms.