Could very well be that your descended from a ridge runner. That's what the families are called that settled along the edge of the Appalachians and then moved south and west. Of course you know its in Johnson County where Loretta Lynn was born (Butcher Holler) and used to be called Paint Lick. Go to:
http://www.rootsweb.ancestry.com/~kyjchs/inquiries-form.htm
That's the address for the Johnson County Historical Society and Genealogical Society. They advertise help by mail for $5.00 (very reasonable) but they'll only answer 2 questions. I'd ask them for the address of anyone else researching William R. Remy and a list of his children (and their birth year) if they have them. From the address we can attach outselves to another researcher and maybe join in with their research form moviing both forward and backward (genealogists love to come in contact with others in the same line - it helps fill in their charts and gives them a chance to show off what they have) and from the list of chidlren and birth years we can start calculating ages toward 1850 (the year the census published the name of everyone living in every household and the name of the state they were born in). With that information we can maybe link into where the family moved after Kentucky. If they were true ridge runners it could be Georgia, Alabama, Louisianna, Texas, or even Arkansas. If not, they may have moved north to Illinois or Iowa or may have gone with the first settlers into Missouri. Be sure to make contact with the Johnson Society. Sometimes they'll have huge files that might contain great amounts on individual families. They could well be a Daughters of the American Revolution repository. An interesting story I found on Paintsville - they passed a law prohibiting the flying of both the Union and Confederate flag at the start of the Civil War. It didn't take long for them to be overrun by the South.