It seems you have John (Andrew's father) death before Andrew is born in 1710. The John you reference as his father must have had a son also named John that was Andrew's father. I have found a John Gregg (1168-1738) I think is the correct one. This John married Rachel (no last name) and they produced John and Andrew. Rachel passed before John immigrated to America and married Elizabeth Cooke (1672–1738) and they produced six additional children.
This is I think the correct progression of this Gregg line.
It makes sense that John and Rachel would name their first son and only daughter John and Rachel.
A[dam] Boyd Hamilton [1808-1896), author of "Historical Memoranda. Middletown-on-Swatara." [Harrisburg, PA. January 1878. 20 copies printed 1879. Author gave one copy to Historical Society of PA.]. Hamilton included an autobiographical sketch by Andrew Gregg (the junior) [1755-1835] which was written probably after Gregg's retirement in 1823. Gregg died in 1835. Hamilton added other information. This compiler (familydog-DEM@hotmail.com) in October 2021 has added s a few bracketed items for clarification, especially of pronoun usage.
Here is Andrew Gregg's autobiographical sketch, with some omissions and reformatting. For readability, this has been broken into paragraphs:
"My [Andrew Gregg's] parents were natives of Ireland. My father whose name was Andrew, was born in the liberties of Londonderry, where the family resided. His father's name was John . . .." "My grandfather [John Gregg] had three sons, John, David and Andrew, and one daughter named Rachel."
(Paraphrasing:) John (the junior) stayed in Ireland and grew wealthy. Andrew (senior), David, and Rachel married in Ireland before leaving on the same vessel some time around 1720. David continued the line in New Hampshire. Andrew Gregg and Solomon Walker, Rachel's husband, did not want to live in New Hampshire and so set out for Philadelphia by way of Boston. They landed at New Castle, Delaware, in the early 1720s. After a winter there, they moved to Chestnut Level in Lancaster County, PA, where Andrew (senior) made an "injudicious selection" of land to take up. His first wife from Ireland died at Chestnut Level, leaving Andrew Gregg with John, James, Rachel, Elizabeth, Margaret, and Jane. In two or so years, more or less, Andrew married his second wife, "Jean" (an old variant spelling of "Jane") Scott. Jane's sister Elizabeth Scott married David Montgomery and moved to Virginia.
Around 1748, Andrew sold his claim at Chestnut Level and moved next to Swatara Creek where he considered purchasing land. Next, he crossed the Susquehanna River and was purchased a warrant for a survey of about 300 acres on Conodoquinet Creek. Andrew (junior) was born in 1755 at the Conodoguinet house. In 1785, after his father's death, Andrew Gregg (junior, the narrator) moved to Harrisburg where he met and married Martha Potter, daughter of (General) James Potter. They had eleven children between 1788 and 1811. In 1789, they moved to "Penns Valley", Centre County PA.
"On the settlement in Chestnut Level becoming sufficiently numerous, they formed a Presbyterian congregation, built a meeting house, and invited Rev. Mr. Thorn to become their pastor. He accepted their call, and in organizing a session my father (Andrew senior] was elected to be a member of it and continued so until his removal. Mr. Thorn's certificate of this circumstance is somewhere among my [Andrew Junior's] papers."
"My [Andrew Gregg's] mother's maiden name was Jane Scott."
"Her father, Matthew Scott, lived in the county of Armagh, in Ireland, from whence he migrated to this country and settled in Chestnut Level, shortly before the death of my father's first wife. His [Matthew Scott's] family at the time of his arrival consisted of his wife, two sons, viz: Moses and Thomas, and four daughters, viz: Elizabeth, Margery, Jean (my mother), and Fanny."
Andrew Gregg (junior) stated that in his family home was a sword which his mother (Jane) told him had been used by her grandfather (Matthew's father) at the Battle of the Boyne as well as an espontoon [half-pike] which his father claimed "he" (presumably Andrew the senior was also referring to wife's grandfather) carried at the battle which took place in July 1690.
Hamilton continues in his own voice from this point, relating that Andrew Gregg (junior) moved to Harrisburg in 1785 and met his wife-to-be Martha Potter. He was a pollical figure on the state (Secretary of the Commonwealth and in both branches of the PA Legislature) and national level (US Senator).
Jane Gregg Father is listed as William Scott of Ireland in Pennsylvania Genealogies : Index of Surnames - “Gregg and Curtin” by Andrew Gregg, Jr. Page 291.
https://www.ancestry.com/sharing/4379276?mark=7b22746f6b656e223a225...
Otherwise details are the same as in msg https://www.geni.com/discussions/171687?msg=1513134