Hi, Kelly!
I would suggest contacting Disney directly if you have specific dietary requests. As you will read
HERE, Disney does its very best to accommodate all allergies. There are email addresses listed there where you can contact Disney Dining with your concerns.
You should also feel free to ask for the chef at any restaurant. Many times I have seen the chef come out to speak to guests about ingredients and food preparation to ensure the safety of everyone (plus it is a great chance to get your kids' picture with the very talented Disney chefs!)
Read through the highlighted page above, and make sure to mention your dietary needs when making dining reservations, when being seated, and when ordering. As a parent, I feel you can never be too cautious! The cast members are well informed and will be accommodating to your needs whenever possible.
Wishing you and your Mouseketeers a magcial Walt Disney World vacation!