The deluxe dining plan works the same for kids as it does for adults. Kids (as well as adults) receive a resort refillable mug valid for length of stay, 2 snacks per night, and 3 credits per night that can be redeemed for quick service or table service meals. For table service meals, kids are generally supposed to order from the kids menu, though some people have had luck with their kids ordering from the adult menu. I wouldn't count on that though. For restaurants that are 2 table service credits, they would take away 2 adult table service credits for every adult meal purchased and 2 kid table service credits for every kids meal purchased. A table service kids meal includes a kids beverage, kids appetizer, kids entree, and kids dessert. There will usually be separate options for kids apps and desserts than what is available for adults at most restaurants.
