Our youngest was 2 years 7 months on our Wonder cruise in August. It was a wonderful age for cruising! Your DD will have lots of fun.
About Flounder's: our DS normally cries and protests for a while when being left with caregivers he does not know, but at Flounder's he was happy as a clam!

The CMs were just fabulous with him. They had all sorts of tricks to get him settled in and happy. We left him there one time, just for a couple of hours, but after seeing how much fun he had there we wished we had signed him up for another time as well. It was WELL worth every penny of the $6/hr fee. I'll bet your DD would enjoy Flounder's even though she wouldn't be with her cousins. Be aware that Flounder's is open only certain hours out of the day, and don't forget to go there early on embarkation day to request your time slots.
If I were you I wouldn't "push" potty training for the purpose of trying to get DD into the Club. I'm guessing it's unlikely such a young child would be allowed, but of course if your DD does end up being potty trained in time, and you felt the Club activities would be age-appropriate for your 2-year-old, you could always ask. Remember that even if your DD is not enrolled in the Club you can accompany her to activities there--spending time with our 2-year-old during "slide time" and other activities in the Club was one of the highlights of our trip! What a fun place for kids (and parents)!
As for Nassau: We didn't feel up to doing an excursion with our 4- and 2-year-olds, so we just had a great time walking around Nassau, looking around and shopping. We were glad we had our lighweight stroller for DS2 since the traffic and crowds were a little heavy and we wouldn't have wanted him wandering around. The boys enjoyed the straw market, though it was a tight fit for the stroller. All the people were most kind to us and our kids, and generally not pushy at all. We took lots of pictures, bought some T-shirts and postcards and beaded necklaces, and headed back to the very pleasantly uncrowded ship.
Castaway Cay was perfect for little ones. The water was so calm and our 2-year-old loved watching the little minnows and collecting seashells. Get off the ship relatively early to get a seat in the shade--you will need the shade! I rested in the shade and sipped a Konk Kooler while DS2 napped beside me in the afternoon--PURE heaven!

Also, if you have room, take your own sand toys. We didn't, and ended up buying outrageously priced ones there on CC! I think it was something like $10 for a little pail and shovel.
Sorry that was so long. Hope I helped a bit. Have a fabulous cruise!