Let me say up front that I personally like SeaWorld very much but keep in mind that a great deal of the attractions at SeaWorld are shows. You need to get to the shows say 10-15 minutes in advance (More for the Shamu show) and then sit through a 30-35 minute show. I don't know about your 3 y/o but when my boys were that little there was no way they were sitting still to watch anything, no matter how enjoyable, for that length of time.
My vote is for either of the Universal parks. If you go to IOA they have three interactive areas for the kids, If I Ran the Zoo in Seuss Landing, Me Ship the Olive in Toon Lagoon and Camp Jurassic in Jurassic Park. Just keep in mind that there are some water activities in each of these so bring a change of clothes. The downstairs area of the Jurassic Park Discovery Center is also great for the kids. There is a section where the kids can watch "dinosaur" eggs hatch, which my kids have always enjoyed. Seuss Landing's attractions are all wonderful for young kids. The Flying Dragon in Lost Continent is a family coaster along the lines of Goofy's Barnstormer at MK.
Should you choose USF, the Woody Woodpecker Kidz Zone is loaded with things for kids to do. The Barney show is just wonderful for the little ones and there is an indoor playground at the show's exit. (It's also accessible without seeing the show). Feival's Playground is in the WWKZ as well and then there's the Curious George play area. Once your kids get here, you will have a hard time getting them out, and trust me, even the 13 y/o will be happy here. The CG Ball Factory is addictive even to the older ones. The water area of CG will get them SOAKED, however, but a great deal of fun. The ET Adventure is in WWKZ also. Up front at USF is the new Jimmy Neutron attraction which also has an interactive play area at its exit. Across the street is the Shrek 3D attraction, which is wonderful for the whole family.
Overall, my vote for your whole family goes to USF/IOA.
Have a wonderful time no matter what you choose to do.