We went on the 3-night cruise last July with DS (almost 3 at the time) and DD (5 months at the time).
We didn't do any excursions in Nassau.
We used Flounders once, from 10 PM to midnight on the second night. It was nice, but we really didn't enjoy being away from our children.
We had the late dinner seating. DD slept in the stroller every night, next to the table.
DD sleeping through dinner DS handled it very well. We got him pizza and ice cream from deck 9 every afternoon to help him make it through until dinner time. He enjoyed playing with the crayons and placemats, and we brought other diversions, such as Hot Wheels. When he got restless between courses, one of us would take him for a quick walk.
DS at dinner If you look at the very bottom of the picture, you can see a die-cast toy of the ship that he absolutely loved (and still does).
We tried taking them to the Mickey ear "fountain," but they didn't like it. Personally, I found the pool area to be a little too crowded and crazy for little ones. There were a lot of unsupervised kids running wild. It probably wouldn't be bad before 9 or 10 AM. I did bring DS to the Oceaneers Club to play with the toys. You can bring your toddler, as long as you stay with them. He really loved that.
He didn't like the characters or the shows, so we spent a lot of time exploring the ship. He really loved the stairs and elevators.

A great thing for toddlers is a small ball for them to chase. We found the hallways by the nightclubs to be a great place for this during the day.
We really had a great time just being together as a family, without having to deal with neverending housework and cooking. It wasn't as important to us to have things to do. We were more focused on just being together. I think most toddlers probably do enjoy the characters and shows, though.
Both of our kids loved CC. We had some empty yogurt containers (we use them for Cheerios and other snacks) that they used in the sand and water.
playing in the water on CC
HTH