In my file I have a Joseph Cawthon, Cawthron, b. 3/19/1828 Tn., d. March 30, 1895 Mountain Grove, Mo., ( I assume it was in Mountain Grove, that is the day written in the bible I have for his death) He married a Nancy J. Shive (2nd marriage) 11/16/1852 in Adair Co., Ky. His father was Martin Bird Cawthon. He had a brother Dabney E. b. 3/5/1832, Tn., d. 2/15/1884 Dent Co., Mo. I found Joseph and his wife Nancy in the 1880 census in Mountain Grove, Mo., I am not sure when they got there. They were in Metcalfe Co., Ky. in 1860 with two children Adaline and John. I have not found them in the 1870 census.
Adaline was married to a Frank Hayes in 1880 with several children, among them my grandmother. Therefore Joseph and Nancy J. were gg grandparents.
I hope this helps, if I can do more please let me know.