The coincidences of name are remarkable, but I don't think that your family is related.
Reuben ALEXANDER b. 1774 m. Jane Allen WILSON in 1796 and they moved from North Carolina to Indiana in 1817 after having spent a year or so in Kentucky. They did have a daughter named Sophronia who was b. 1805 and who m. William JOHNSTON or JOHNSON.
Reuben & Jane ALEXANDER also had a son named Reuben who was b. 1818, but in 1880 he was living in Thurman, Fremont County, Iowa. His first wife was Mary ALEXANDER (widow of his older brother) and his second wife was Keziah CRISWELL. To the best of my knowledge he never had an adopted daughter named Sophrona.
Reuben ALEXANDER b. 1823 in Ohio who had a wife named Hannah can be found in the 1850 census for Monroe township, Ashtabula County, Ohio. Next door to him was Phineas ALEXANDER who was b. 1783 in New Hampshire who I would guess was his father. Living with Phineas was Stephen ALEXANDER b. 1809 in Vermont and a wife, Caroline, b. in New York. Perhaps your Sophrona belonged to this group.