If your children are very young, I would forego the Disney/Orlando thing and head to the beach. My family fave is Amelia Island Plantation Resort near Jacksonville. Sanibel and Captiva islands are both great spots with huge white-sand beaches with gentle surf ideal for non-swimmers. Other resort areas along the west side of Florida will be nice, too, places like Naples and St. Pete/Clearwater. I'd skip the Keys with young kids as there's more driving involved. Not sure where you're flying from, but loads of cheap flights to Jacksonville, Fort Myers, Tampa, and yes, Orlando.