Hi Jessica!
I completely relate to picky eaters, we have a few in our family as well. One of the greatest benefits of staying in a villa is the use of the full kitchen (or kitchenette if you are in a studio) for those quick meals that picky eaters may find comforting. Upon arrival I would suggest stopping by the Screen Door General Store down on the boardwalk, they have a nice selection of groceries, beverages and dry goods.
Once you are at the park, picky eaters don't fear! There are plenty of dining options to suit any taste. Every Walt Disney World theme park has a variety of dining options including table service, counter service, and snack carts. The park maps available at your resort and at the park entrance will list the dining options available in each park.
If you want to try to pre-plan your dining experiences, check out the
Dining Finder , it's a very helpful tool for finding the dining options may be best for your family. You can search by cuisine, price, dining experience, and location.
Have a great trip!