Welcome aboard, Gretchen! You must have a magical Disney cruise in your future!
If you've never been to Nassau before, one of the most popular places to visit in the Atlantis Resort. Since you have a really little one, I'd recommend the
Atlantis Beach Day & Discover Atlantis Port Adventure. This is for guests of all ages, and has something to offer everyone. You'll get to tour the resort and the "ancient dig" of Atlantis at your own pace. This replica of an actual archeological dig site has fun underground passages and windows peeking into an underwater world. Children love it! You'll also have access to the beautiful beach at the resort where your kids will enjoy playing in the sand and splashing in the water. There is lots of shopping available, and even just wandering the grounds of this amazing resort will be interesting for your children. You can choose your own return time as the day goes on, so this is really a laid back adventure you can enjoy on your own time!
Taking one of Disney's Port Adventures means that they take care of all of the details, which I think is especially important when you have two young children with you. All you need to do is show up! They'll get you to and from Atlantis and you can spend your day however you'd like at the resort.
Take a look at some of the other
Port Adventures offered in Nassau. Once you select Nassau, then scroll down on the left side and choose the 0-2 age range, to ensure that you're only viewing adventures on which your 18 month old can join you. The Blue Lagoon Island Beach Day is another one you might consider!
Stop back and let me know if I can help with anything else before you set sail, Gretchen!