I don't have experience with your wife's condition, however, I've been a vegan (so no animal products at all) for many years, and WDW is an absolute vegan haven, with so many food choices practically everywhere. There's a terrific
WDW vegan food blog with lots of reviews of restaurants in the parks and at the resorts. It's been very helpful to me.
Also, note that TS (sit-down) restaurants are tremendously accommodating to all dietary needs. The executive chef will come to your table and discuss what you can and can't have and often come up with something that isn't even on the menu. And note that there are many off-menu items at all (I think all) the TS restaurants.
Good luck to you and enjoy your trip!