Keep in mind that schools in Florida typically close for summer in early June; some schools in other states close even earlier. Expect crowds to be heavy from Memorial Day on. Late August, meanwhile, can be quieter as many kids are already back in school.
See lots of Florida family vacation ideas: Orlando, of course; and many beach areas. In northeast Florida, Amelia Island has giant Amelia Island Plantation resort, and a Ritz-Carlton; beaches, nature outings, historic town and fort. Further south-- and just an hour from Orlando -- the Space Coast offers the Kennedy Space Center, miles of beaches, nature refuges, cute towns, and affordable prices.
Keep going south: on the Treasure Coast is Disney's Vero Beach, and -- nearby but inland-- a Caribbean-style all inclusive resort, Club Med Sandpiper, with trapeze, sailing, golf, and outstanding kids programs. And also: the Everglades, Sanibel Island, Clearwater Beach / St. Pete area, the Emerald Coast...
- continue to Southeast US