Hi there,
I have spoken to friends in Florida who advised me against going to the parks on that day. We still went although do something slightly different like, rise early and go to the BB water park for opening time spend 5 hours there, then crazy golf at the Winter/Summerland, good fun!!!
Leave to go back to your hotel and rest then how about a nice buffet meal at the Trails End Buffeteria at the Fort Wilderness resort, this is one of many little gems at the Campground. You could spend the rest of the day there at the Tri Circle ranch, carriage rides,walks,the nightly Hoe Down making marshmallows with the kids. Another overlooked show is the hoop de doo review, book early though.
At the end of the night take a boat from the FW to the Contemporary to the TTC then connect with the Epcot monorail and be there in time for the Illuminations. If you want more food then consider either a quick fish and chips from Harry Ramsdens or try exiting the park at the International gateway and visit either Beaches and Cream at the BC or a Boardwalk eatery
Just a couple of tips, although I avoid the "Parks" on days such as these.