Also be aware that just mentioning the vegetarian thing to the servers will help out. We had a vegetarian friend at the 50s Prime Time not too pleased w ith the vegetarian options on the menu. So she ordered a turkey sandwich without the turkey. After we explained to our server that our friend was a vegetarian, five different choices were provided that were not on the menu, including a veggie burger. For table service, if there is a kids meal that interests her, chances are she'll be able to get it. And that's a definite at the counter service places.
Also for table service, if she sees different sides that interest her like a baked potato listed with one meal and rice listed with another, she can just get the sides as a meal. And there's always vegetables of some sort as a side in every table service place.