It's been a long time since your message was posted here, and I'm sure you have made many corrections and additions, but just to make a few here on this forum:
William Brockinton, b. 1688, married Sarah Griffin in South Carolina in 1715.The marriage is listed in the parish register of St Thomas and St. Denis.I believe he was born in England, not Ireland, but have not found good proof.
William and Sarah had, among others, John Brockinton (not a captain) who married Mary BARR - not Drew.Nathaniel Drew was her stepfather.HEr father was Gavin Barr, who died aboard ship on the way to SC.
John Brockinton and Mary Barr had a son named John Brockinton b. 1754, and it was he who was a captain in the Royal SC Militia.It was also he who married Martha Screven Fowler, daughter of James Fowler and Martha Screven.
John Brockinton, the Tory, had a son named John Brockinton who married Sarah Nesmith.
John Brockinton above and Sarah Nesmith were parents of Samuel Brockinton who moved to Mississippi and then to Arkansas, and it was he who married Eliza Elmirah Arnette.
Among their children were Josephine who married Mr. Boyd and a son named John Samuel Brockinton who married Melissa Brown.