You may have some interest in the following.
Research shows that the William Davidson who married Martha Baker (the parents of Mrs. Jane (Davidson) McCartney and her siblings) was almost certainly from a branch of the Davidson family that is represented by DNA "Family 10" at www.davidsongenes.org
(and I am also a member of DNA "Family 10"....but through a different branch of the family). I have traced this Davidson family back to the David and/or William Davidson who both died in James City Co., VA in 1687. That David Davidson left a "naturalization document" that was dated in 1686, and it showed that David was born in Holland. The "DNA signature" of this Davidson family shows that we have a "Viking heritage," so this Viking family probably settled into the area of Scotland and took the "Davidson" surname many centuries ago. Holland was the number one trading partner with Scotland in the 1600s, and many Scots lived in Holland as a result (and there is still an active Scottish Church in Holland today).
Note: I have no proof that the above David Davidson was definitely related to the William Davidson who also died in James City Co., VA 1687, but there is certainly a fairly good chance of that. David Davidson was married to a Sarah Unknown, and she MAY have been a Miss Hamblin or a Miss Hunt, based on the names of the two men who helped her with the estate after her husband David Davidson died in 1687.
It appears that the much later William Davidson who married Martha Baker (Martha lived in Prince Edward Co., VA before she married) was PROBABLY the William Davidson who was the apparent son of the David Davidson who died in Buckingham Co., VA around 1798. The 1764 Buckingham Co., VA tithe list showed that a male named William Davidson was living in the home of that David Davidson (and William was mentioned only because he was apparently old enough in 1764 to also owe a tithe of his own).
Mrs. Jane (Davidson) McCartney's brother William Davidson, Junior was the father of William Baker Davidson (who married Elizabeth Chapman Hunter). William Baker Davidson graduated from West Point, and he was a Captain who was killed by Indians on Christmas Day in Indian Key, Florida in 1840 during the Seminole Wars. Two of the sons of Captain William Baker Davidson were General John Wynn "Blackjack" Davidson (also a West Point graduate...John fought for the Union during the War Between the States) and Commander Hunter Davidson (a Naval Academy graduate...Hunter fought for the Confederacy). While still a Lt., Hunter Davidson was the onboard officer in charge of the armament on the ironclad "Merrimac" during its famous battle with the ironclad "Monitor" in 1862. You can "Goggle" Hunter Davidson and read about some of his exploits. Hunter was also a friend of James Whistler who painted "Whistler's Mother," and there is a letter (available online) from James Whistler to Hunter Davidson. Hunter Davidson moved to Paraguay after the war, and he started a second family down there. General John Wynn "Blackjack" Davidson was assigned to "control the Indians" in the western states after the war, and he died a few days after his horse slipped on ice and fell on him.
Thanks for the info that you posted, and I wish you the best of luck with your continuing research on the McCartney family.