I took my daughter to Disney when she was 2 and 1/2. She loved it. Under 3 was free back then. I assume it probably still is, so you'd only have to pay for yourself. My daughter hated Sea World at that same age.
I stuck with Magic Kingdom, because that one is geared for little ones and they may actually be familiar already with some of the characters like Mickey and Winnie the Pooh. My kids found the other parks to be boring when they were younger, plus they aren't tall enough to get onto a lot of the rides in the other parks. Animal Kingdom is okay, but it really only takes about a half day to see the whole thing.
Also, I recommend getting a room in the park. If you go off season and stay at one of the budget Disney hotels (Pop Century, and All Star Movies, Music, or Sports) the prices aren't bad, and they are very whimsically decorated. I think my son liked the resort as much as the park. Plus you get free bus transportation to and from the parks' front gates which is really nice with two tired toddlers. Check out their website because they have discounts for FL residents for both the hotels and tickets. It also allowed me to take my daughter back to the hotel in the afternoon for a nap and/or some downtime. That really made the difference I think. You also get free parking at the parks on the days you are a guest, in case you want to drive. Try to go with the idea in mind that you just want the kids to have fun and don't care if you get to see everything.
The other thing I recommend is renting a stroller from the park. I think a double stroller is $13/day and it's totally worth the expense. You don't have to worry about losing it, if you do, you can just take your reciept up to the rental desk and they give you a new one. Plus you can get one at any park that day without having to worry about lugging anything around on the busses or monorails. The only drawback is that you can't take it outside the park, so the trip from the front gate to the bus stop at the end of the day might be torturous for the three of you.
Oh yeah, bring rain ponchos. You will likely need them. Get the $1 disposible kind. Also, try to go off-season. Little people hate waiting in lines and hot weather. They also don't mind if you bring food or drinks into the park, so you can make sandwiches and drink boxes and carry them in your backpack (better than a diaperbag if you can to carry people around also). We usually drive to McDonalds outside of the park for breakfast before hand also.