I cannot address the proof that Eleanor Alexander who m. Samuel Rankin was a daughter of James Alexander who d. 1753 in Rowan County and his wife, Ann. The best person to contact for that information would be Robin Rankin Willis who has posted several messages to this Forum. She has done meticulous research on this Alexander and Rankin line.
I do not believe that Robert Rankin who m. Mary Withrow in 1769 was a son of Eleanor Alexander & Samuel Rankin. I don’t remember the marriage year of Eleanor & Samuel, but I don’t believe that they could have had a son of marriageable age in 1769!
Mary (Withrow) Rankin’s father, John Withrow, wrote a will that was proved in 1792. In that will he gave to his daughter, Mary Rankin, “the Negro wench, Bash” and “my plantation at Beals Springs joining Robert Rankin’s old plantation” at her mother’s decease. From this we can say that Mary (Withrow) Rankin was still living in 1792. We do not know if Robert, her husband, was still living.
I do not believe that Robert Rankin who died in Caldwell County, Kentucky in 1816 and who had a wife, Leah, who survived him was the same Robert Rankin who m. Mary Withrow. At least, I have never seen any documentation that he (1) divorced his first wife, Mary or (2) deserted his family in North Carolina.
I would be willing to share more thoughts on these families if you would like.