It looks most likely that the parents of Charles below are BRYDEN WILLIAM & JANET HAIRSTONES / HASTINGS who married 26/07/1822 Morton
Children all born Morton. WILLIAM 20/01/1822, JOHN 14/03/1824, JAMES 15/05/1827, CHARLES & MARY 18/09/1831
1841 South Drumlanrig St. - W. Side, Morton the above family except no William senior or James.
So William most likely died before 1841.
No trace of Charles in 1851 but the marriage you mention below.
Charles Bryden to Eliza Clarke
Marriage Q3/1858
Whitehaven, Cumberland, England
1861 - Main Street, Egremont
BRYDEN Charles Head 29 Iron Miner /news Agent SCT -
BRYDEN Eliza Wife 29 YKS Leeds
BRYDEN Jessie Dau 1 CUL Egremont
Your original post mentioned you were unsure which of the two Williams born to Robert & Agnes was the correct one.
Given the names of William & Janet’s children I do not think it was either. Assuming they followed the Scottish Naming Pattern their eldest son would be William, though not all did, however I would have thought they would have named at least one of their sons Robert. Have you considered the birth below?
BRYDEN WILLIAM WILLIAM BRYDEN/JEAN GLENDINNING 06/05/1798 Tinwald
Another way to check might be a look at the 1874 death of William Bryden there maybe some information to help?
Regards Colin