All I can add is this very nice story from "Motherwell 60 Years ago and Now", written by a member of the King family back in 1910. So he is writing about his childhood in the village from the 1840s onwards. The Kings were well known and one of them, who had a builders business, built the first two-story building in the village, the Motherwell Inn. This was also at the Cross.
If you can figure out when exactly the David Hamilton in this story was married I can pencil it into the margin of the book. The story is on the right-hand side of the scan, so you'll have to scroll over.
I should add, for all those who know Motherwell, he is describing the Cross at Muir Street. "Clyde Street" is now Hamilton Road.