What about a day at Discovery Cove? Your twins would be too young to swim with the dolphins (minimum age is 6) but it would be a wonderful, relaxing, tropical day for everyone nonetheless. Maybe give you that island getaway feel while still being in Orlando.
Their Grand Reef is so much fun....swimming with all the rays and tropical fish. The Freshwater Oasis features Asian otters and marmosets. You could hand-feed the birds in the free-flying aviary. The lazy river is superb, with varying depths, waterfalls, a cave, and more (and it takes a full 20 minutes or more to do a full rotation). There is a gorgeous beach that's great for building sandcastles. And to top it all off, everything is included....parking, breakfast, lunch, snacks, beverages (even alcohol), a family photo, sunscreen, towels, wetsuits, lockers. You literally need to bring your camera and that's it.
As an added plus.....14 days admission to both SeaWorld and Aquatica are complimentary. Both fabulous parks that are well worth a visit (more than once).