i think you're at one of the absolute BEST resorts to spend an off day!!!!
i've stayed there but once, but there's tons to do- most already mentioned. if you can do any of the special early morning things, of course do them. but, if not, sleep in an hour or two. sign up for the hidden mickey tour (make a resi in advance), hit the pool. and btw, they have one of the best pools areas on property! lots of activities, a bar, some wildlife, and an incredible setting!
not to mention the theme doesn't end at the pool area. go. wander about. rent a bike check out the nature trails! there of course is an entire lake to interact with- fishing, boating, para sailing..... heck, just ride the boats for the view!
not to mention, there are obviously a few things you could take your family to enjoy off resort. the boardwalk is excellent!
but if you can't find something to do at the wl, well.......
enjoy!!!!!