With table service, you should have no problems. Counter service is limited to what they have. They don't have a chef there to prepare something not on the menu.
At the Animal Kingdom, Pizzafari has spaghetti and meatballs for a kids meal but she can get it without the meatballs.
At the Studios, the Studio Catering Company has the aforementioned mac and cheese and PBJ.
At Epcot, you could switch meals at the Lotus Blossom Cafe which is great for vegetarians.
Cosmic Ray's has a salad with chicken but she could take that off.
And don't forget that you can always get fries all over the park.
Be creative. Switch meals. Get her an adult meal and you share and have her kids meal. Get a bunch of stuff and everyone share.