Hi Debbie,
You are not alone and I completely understand your concern as my Son is also a picky eater.
If nothing on the adult menu appeals to your Daughter at any of these restaurants, she will be able to request something from the children's menu instead. In most cases, you will find that she will be given a larger portion than that which would normally be given to a child.
If you are really struggling, it is worth asking your server if it is possible for her to have something which is not on the menu but is fairly easy to make, like a sandwich or toastie for example. Whilst this can't be guaranteed you will find that Disney are very accommodating to children who are picky eaters.
The only thing that I would say is that when you are using the Disney Dining Plan, you don't get the best value for your money by using adult table-service meal credits to purchase children's meals. It may be worth considering paying out of pocket for your daughters meals in these instances which will mean that her unused adult table-service meal credits will be able to be used by someone else in the family. Perhaps you could use them to treat yourselves to a
Dinner Show or
Signature Dining experience which require two table-service meal credits per guest?
I hope that this information has been of help and wish you a magical holiday filled with memories which will last a lifetime!