Hi, Cheri!
You are going to have the most amazing time staying at Disney's Beach Club Resort! It's truly beautiful there and you will be just steps away from the International Gateway entrance of Epcot where you will have all kinds of restaurant choices for your little picky eater, I'm quite certain that his choices will be ample in the World Showcase.
After looking at the menu from the
Beach Club Marketplace, the Quick Service eatery just off the Beach Club's lobby, I see Flatbread on the adult menu and Pizza on the kids' menu. I'm sure if you spoke with the Cast Member when you place your order, they'd be happy to leave the sauce off of either one of those for your son.
While there are a lot of restaurants that are included on the
Disney Deluxe Dining Plan, Shula's Steak House at the Walt Disney World Dolphin Hotel is not one of those. I've include a link to the brochure so you can see the most current list of restaurants that accept the Dining Plan.
I sure hope this helps, Cheri! Please stop back by if we can help with any other questions you think of!
Wishing you Pixie Dusted vacation planning!
~Jackie