I am not sure that this is what you are looking for or even if it is a match, but I have some information on the APPLEWHITE family of Waller Co., Texas.
I recently found a marriage certificate for E. C. APPLEWHITE and Annie BELL dated 13 April 1886 and officiated by John RENFRO, Local Elder in the M.E.C. This has yet to be proven, but I believe this to be Edward APPLEWHITE, second child from the marriage of Arthur APPLEWHITE and Mary Jane ALLEN. Arthur was a physician (originally from VA and later TN before moving to TX) and this marriage was his second.
Your query seeks information regarding Edward's daughter, Eleanor. Regrettably, I do not have information contemporaneous to this generation. However, I would very much like to compare notes on these earlier generations if you find that my assumptions above are correct and this is the same Edward.