Hi there Martha~
I believe there may of been two William Farmer's too. As for Minnie E Farmer, my Grandmother, I do know quite a bit. I was born in 1949 so I don't remember her (she passed in 1946, but I am aware of her 11 children and I have her death certificate but I need to get her Birth Certificate (DOB) 27 Nov 1863 if I can.
As for E S Farmer I am attaching a Land Record I found and it confuses me. It Definitely say Dr. E S Farmer, I have marked it with a red arrow. I have always thought that he was a large farmer and stock dealer so this confused me. I know my Dad and Brother both had the middle name of Stanford so I have always paid special attention when I see it in the Farmer line. I do know that William, Minnie's Father was indeed in Bordley, Union County, KY and the Bradburn's were mentioned in the History of Union County, KY. So, I do know that is the right William I am trying to follow. I am so thankfull for your help, dear Martha!