Kites? I thought you were asking about, umm, kilts. No, kites are NOT allowed anywhere in Lake Buena Vista. It's a kite-free zone, so sorry.
Well, if you were asking so that you could occupy DD's time, instead of kite-flying, here are some things you can do with her to fill some downtime. These are described in more detail on the the first page:
~Hidden Mickey Scavenger Hunt. Sheets are available from the concierge/front desk
~Cub's Den has activities in the afternoon
~There's a playground on the beach
~Bike rentals
~Pony rides at FW and stables
~Arcade
~VWL has chess/checkers and train models off the lobby
~Take a walk to FW. There are trails in the woods where she can see critters, it starts behind the marina and there's a concrete trail near the bus stop if you want to ride bikes
~Play in the sand on the beach
~Take the boat over to CR and watch the monorail or go shopping
~Rent a boat and take her for a ride
~Tour the grounds inside and out