Alexander McArthur's first wife Catherine McKay McArthur's gravestone said she was survived by 9 children. Gravestone in Oyster Point - "Sacred to the memory of Catherine McArthur, wife of Alexander McArthur, who departed this life 27th of December 1807, age 37 years. Leaving a husband and 9 children." I am missing one child.
There was a will for an Alexander McArthur, Lot 14, signed on 9 July 1839 but proved in 1870. Named in this will, in this order, were Dugald, Hugh, James, Alexander, Archibald, Robert, Mary, Jane, Flora, Elizabeth, and Neil. Most of the children received one shilling, and Neil (Neile) inherited the farm. George and Thomas Lee were executors. PEI Probate Records, Wills not recorded," A-M, McA (misc. dates between 1786?-1930?), on familysearch.org.
No daughter Catherine named! However, it wasn't unusual for the first daughter in a second marriage to be named after the first wife. She might also have been Nancy's daughter before her marriage to Alexander - this might explain being left out of the will, and for the records where she was called Catherine McLaughlin.
One source says that this Catherine or Kathleen married John McArthur 6 April 1831. There is a marriage for John McArthur and Katherine McArthur in the Presbyterian Church, Richmond Parish records; her date of birth was estimated, assuming she was about 21 when she married. John died, leaving her a widow with 5 children.
Some family trees say that John's wife was Catherine McLaughlin, based on their son Neil McArthur's death record. There are several possibilities. Neil's family might have mixed up his mother and his grandmother's maiden names. Catherine might have been born before Nancy's marriage to Alexander.
Another possibility is that she was the daughter of Hugh McArthur and Betsey McLaughlin.
There was also the Catherine McArthur, widow, who married Robert Lynch in 1845, and had three daughters. To add to the mystery, her marriage record said Mrs Catherine Matthews - perhaps a typo?