Hmm... well we just didn't invite any kids to the wedding, but I think your problem is that they're invited to the ceremony but not the reception?
The classy, spendy way you could do it is to have a room where people can drop off their kids and there's a sitter and activities and stuff...
Or, I guess if the invite has a separate card for the reception, it could say "Adults only, please" and include info about Disney's various kids clubs and the price of in-room sitting.