You also may be surprised what you kids enjoy. The shows at SeaWorld might pull them in more than you expect. In Pets Ahoy, the animals are very engaging and some of them go over the audience. In Clyde and Seamore (a truly great show!) there is the very funny Mime in the beginning and then the slapstick humor really appealed to my kids. It's not like sitting still watching a screen. Now, I don't know whether or not they'd love Believe (or whatever Orca show is playing when you are there), but lots of kids enjoy sitting in the splash zone, waiting to be drenched even if they are not totally into the show. We missed the dolphin show because of Wild Arctic so can't speak to that one. We deliberately missed A'lure (- it didnt seem very alluring - sorry I couldn't resist!)
Your older kids may also enjoy the rides: Manta (my dd9s absolute favorite in Orlando!), Kraken, and Journey to Atlantis - and Wild Arctic (similar to but not as good as Star Tours). The younger kids may enjoy Shamu's Happy Harbor with the kiddie rides. In fact, you may want to split up in the morning (after feeding the dolphins) to let each group to ride what they want before the lines get awful.
Then you can feed the animals. Dolphins first because it generates the greatest lines. The rays are really, really fun, the sea lions OK, and the sharks - eh. Just watch out for the birds that will steal your fish.
On top of that are all the animal exhibits - like a Marine zoo, which could keep you pretty busy if your family likes those things.
Sea World is HUGE! If you don't plan carefully (especially about Wild Arctic/Shamu show/ Shamu's happy harbor - we foolishly went around the lake 2 times!) you will log more miles than at most of the Disney parks (I think we walked more than Epcot). This would be the reason I would be most concerned for your trying to do SW and Aquatica in one day. If Aquatica is like a Disney Waterpark, perhaps it clears out after 3 (about when you'd be done with SW if you are skipping some shows) and the lines wouldn't be too bad, but you might be pretty tired.