Thanks for your reply. My grandmother was Margaret Carroll Byrd, Arthur's sister, and my father is David. I saw this info posted by someone else, but I couldn't find any way to verify it:
"I am looking for the first marriage for LILLIAN ARENDELL in the years
1885-1893 in Muhlenberg Co Ky,
She married unknown CARROLL..
He must have died before 1897 when she remarried to Samuel P Kinkade.
Lillian Arendell is possibly the mother to EDDIE CARROLL born 1893
This is the little info that I have to date on LILLIAN ARENDELL.
Lillian D. Arendell
Born: 14 Oct 1869 Butler Co,Ky
Died:2 Aug 1924 Muhlenberg Co,Ky
Buried 3 Aug 1924 Oak Grove Cem. Butler Co,Ky
Father Richard Lewis Arendell b.1842 Ky
Mother Sarah Jane Adkins Arendell b.1848 Mo.
2ND Married: 20 Oct 1897 Butler Co,Ky Samuel P Kinkade"
It was posted back in 2000 on another website, so the contact information for the original poster is most likely out of date.
Any information you have would be helpful. I have hit a roadblock on the Carroll side with this possible adoption thing. I am also on Find a Grave, but haven't been able to post a memorial for Lillie since I couldn't remember what cemetery she was in. Feel free to communicate further via this thread or through private message.
Thank you for your help!