I have asked this question in regards to vegetarian meals and have been told most of the TS places will make special meals for people with certain dietary needs or preferences. I have also heard people say they have gotten "adult" portions of items on the children's menu if nothing else would suit. Have you taken a look at the menu section of allearsnet.com? They have a lot of information about the menus there.
What kind of things won't the teens eat? If you are more specific you might get responses from people with experiences similar to yours.
Have fun on your trip. I think you will find plenty for your teens to eat!