In Port Canaveral, I wouldn't trek all the way to the theme parks w/a 3yo. Instead, I'd take the shuttle buses to Cocoa Beach or even go to the Space Center. Does the ship call in Miami still ? If so, I'd check out either Parrot Jungle or the Seaquarium. Little ones like animals (at least my almost 3 yo does)! As for Nassau, check out my article "Back to the Beach" listed on the main family page on this site. It lists a few beaches in the area that are family friendly and that you can take a taxi to.
Hope this helps!
Luisa Frey Gaynor