Oh definitely. One day is plenty.
My big advice is to bring your kids, and maybe yourself, a change of clothes. There are a lot of ways for kids to get wet in that park and walking with wet underwear and socks doesn't make for a good time.
I highly recommend the Pets Ahoy show - I am sure your kids would love it - so many cute cats and dogs. The Clyde and Seamore show is very fun as well. It is really a beautiful park. Enjoy!
One full day will see you doing everything that you want to - its a great place to visit despite all the recent negative publicity.
One thing to remember, it's a place of educational value as well as a theme park
If you've got the time and are interested in either Busch Gardens Tampa or Aquatica, check into combo tickets that include Sea World. These are often deeply discounted far beyond what Disney or Universal do.