Thank you for your response to this question, you have put the spotlight on the most likely incorrect linkage on the tree. As you point out there was a title involved and given the year that the 5th Lord of Belhaven and Stenton died (1777) the Privileges Committee of the House of Lords (UK) became involved in deciding the succession. There was, as expected, rival claims to the title and the Committee decided that Robert Hamilton was de jure the 6th Lord and so his son William was the 7th Lord (1793). That Committee keeps very accurate family trees and there was no consideration of a second son named James.
The error, as you point out, is on the Hamilton-7003 profile and there are a number of managers of that profile including the Scottish Project Wikitree. I will raise the issue with the managers of that profile and hopefully have the second James removed. As pointed out elsewhere the "system" should then fix the DNA issue.
Thanks also to the others who took the time to answer my question.