Hi, Jeanette!
Congratulations on your upcoming vacation with Disney Cruise Line! Since you are sailing in July to the Bahamas, then you're aboard the Disney Dream, and you'll be making at least one stop in Castaway Cay -- maybe two! Therefore, my suggestion is to reserve your "beach time" for Castaway Cay and spend your one day in Nassau touring the area or enjoying the full amenities of the Atlantis Resort.
Although the
Atlantis Beach Day does include access to The Dig and lunch, the use of pools and water slides is not included in this excursion -- the areas are all together and require identification. My standard suggestion is to either book the
Aquaventure excursion, a dolphin encounter or one of the many tours which guide you through the historic sites of Nassau. These are Port Adventures you can't do at Castaway Cay.
For your toddler, you will need to book a reservation for the It's a Small World Nursery. You can do that online at the DisneyCruise.com Planning Center, and there is a small fee per hour/per child. There isn't private babysitting offered in one's stateroom. I hope all this helps you plan. Let me know what else I can do to help.
Have a wonderful day and a magical vacation. Bon voyage!
Andi