Elizabeth Hodges a BATES?

Bill, in an early post, you mention that Missouri T HOLDER is in the household of her grandmother "Elizabeth Bates HODGES" 1860 census Franklin co TN
I cannot confirm thru any records or tree if this woman, Elizabeth was a BATES and I can't find a marriage for her to a HODGES.
My dilemmais that I descend from William HOLDER and Frances Caroline BATES and , for the life of me, I cannot find parents of Frances Caroline.Some
speculate it's Matthew and Unity who were in Franklin co TN at time Frances married William Holder (1840) but Matthew and Unity Bates married 1823, about 5 years AFTER birth of Frances Caroline;so I'm especially interested in the Elizabeth you mention.Can you or anyone else at HOLDER forum help?