It looks like Caldonia's parents were Thomas H. Barrington and Mary Frances Overstreet Barrington. Thomas and Mary Frances were married in Freestone County, TX, on June 30, 1859. The names, place and timing are enough to draw a conclusion, in my opinion. Because they are so consistent with Caldonia's story, the chances of it just being a coincidence is very small. Mary Frances had an older brother, William Overstreet that married a Nancy Jane Barrington in 1854. I have not been able to identify the Adams that Mary Frances married after Thomas Barrington's death. Based on your statement that Caldonia is your great grandmother, I believe that makes you my fifth cousin through the Blakely family.