My DH is on a very low-fat diet for medical reasons, and we also worried about eating in the parks. Here are some things to note:
1. The food in the parks is really not bad. I thought we would have trouble finding something DH could eat, but it wasn't hard at all. Almost everywhere we went there were salads or chicken/turkey sandwiches.
2. You can always ask a CM at the restaurant for information on the item you are interested in. If they don't know, they can ask the chef, or they will ask the chef to come speak with you to help you order.
3. You also can call Disney Dining and ask to speak with the Head Chef. There is one for DL, and one for CA. Chef Ricky (DL) called me back and gave lots of good tips (including the above) for us in the park, and encouraged us to even ask for specially-prepared versions of menu items if necessary. That would require some advance notice, of course, but he said they really will bend over backward to serve you, so don't hesitate.
We actually ate in the park every day, never bothered to have specially prepared foods (though we did bring our own snacks in), and we ate well. Before the trip DH was sure he would be eating only salad greens all week long, but that wasn't the case at all. And just knowing that we COULD ask for help or special preparations if needed set our minds at ease.
Have the person on the restricted diet (assuming it's an adult, or their guardian) call to speak with the Head Chef for ideas on what they serve that fit within his/her restrictions. I was so glad I did!
PS. One more thing: We did not eat at the same place twice during our 8-day stay, and ate most of our meals in the park. So you won't be stuck with one food or one restaurant!
PSS. It's also helpful to review the menus for each restaurant beforehand. They're posted online, and it really helped us figure out where we wanted to eat and what sounded good!