If you have not already discovered the answer to your question, this may help.
I am doing research on my mother's family name, Vaughn. Our family records indicate that her father was James W. Vaughn (b.1885 d. 1928), his father was also James W. (b-1845), his father was not named in the family history, but could have been Jesse Coleman Vaughn. The Jesse Vaughn in you inquiry was married at least one (Nancy Freeman) possibly two times. Alexander and Mariah are indeed his grandchildren.
If you have any corrections or something to add, please let me know. Vaughn Adams