I would suggest you check the census records - they usually state whether a person was of American Indian heritage. Also you might put some queries out on the various web sites for AMerican Indians, especially Cherokee - if you haven't done that already.Several sites have long lists of names (especially surnames) of Indians. If there were a "Layman" or "Layton" from Seveier Co, TN that might be a clue to her parents.
also you might check tribal lists in Idaho to see if they joined a tribe there and received benefits they were entitled to receive. Also his WWII records would probably show if he were part American Indian, unless he didn't want that known and just signed on as "caucasian" - which some do.
I hope you can find out - but it may be difficult. Perhaps the best thing is to try to find out the names of her parents in the local county library records. Our local library has big books with births, deaths, and marriages for the county.