Further to my post saying I was confident that David Hall, miller, of Coppanagh, was a son of William & Arabella Hall of Lattacapple, it has been pointed out that this is very unlikely and I now agree.
William & Arabella's son David was still living with his parents as a "labourer" in the 1821 census. The Coppanagh family have a separate history, indicating they were more prosperous, with more valuable assets, than the Hall family in Lattacapple.
There must be, however, some link between the families to explain the inheritance of shared DNA.