Hi Rhonda,
While character dining may serve fancy food, all of the buffets at the Walt Disney World Resorts feature children's favorites such as chicken fingers, sliders or pizza. The menu rotates with the seasons but most children can find something. The other cool feature is that the children's section is dropped to their height which I think is great. I love buffets because it allows my picky eaters to expand their palates and try new foods.
Trails End is located at Fort Wilderness. This restaurant serves chicken, ribs, pasta and other American fare.
1900 Park Fare is one of my favorite character dining experiences. Cinderella's family makes the meal along with the delicious food. This is a smaller but selective buffet.The salads were unique and delicious without being fussy.
All of the restaurants have sample foods listed on their webpage.
I think your picky eaters will be fine. And if you want to have a chicken nugget, go for it.
Have a magically delicious vacation!
Beth