I was interested in your post. Some names and places are very similar to my ancestors' Adams family.
My ancestor, Hester Adams (1785-1846) was the daughter of Elijah Adams and Hannah Blair. She may have been born in Bedford County, PA, but that isn't certain. Her mother's family definitely lived there. William Blair, father of Hannah, came from Co. Tyrone, Ireland, about 1776, to Bedford County, where he died in 1788. His wife was Hester. Of his children, Alexander Blair lived in Mount Pleasant, Westmoreland Co., PA, in the 1790s, and his son Thomas Blair (1756-1800) did so briefly in that decade.
Elijah Adams came to Kentucky around 1797, and lived in Montgomery County. He appears there in the tax lists in 1800 for the last time. He probably died then (but no court records have survived), and his widow and family went to live with her brother Alexander in Nicholas Co., Ky.
Elijah was born probably about 1760. He was probably related to the Elijah Adams who died in 1799 in Bedford County, leaving a will (this person also had a wife Hannah and has been confused with the Elijah who went to Kentucky). The latter Elijah seems to have had a brother Robert who died in 1828 in Bedford County, and there was a Samuel Adams who was also a contemporary. In short, it seems like your Alexander's father and my ancestor Elijah may have been brothers and that they in turn were related to Samuel, Robert, and Elijah, but how is a mystery.
Did Robert (d. 1810) live anywhere near Mount Pleasant?