Bit of an update regarding David's wife
There are several names popping up. There's the Elizabeth/Betsy Clark Henry gives as his mother in his poor relief application and marriage register, which is the only mention I find of her. There's Agnes Dickson, who appears in the censuses, but she can't be mother to at least some of the children - she'd have been between 12 and 17 when Henry and his brothers James and Hugh were born. The 1851 census shows a 13 year old Henry and then a 12 month old daughter called Agnes, so I'm thinking Agnes was step-mother to the three boys and David had two more children with her (Agnes in 1850 and Mary in 1859).
James's death certificate gives his mother as "Mary Dickson", ms Dickson, informant was his son James
Hugh's death certificate rather unhelpfully doesn't know what his parents' names are, his son William leaving it blank beyond the surname of Dickson. His wedding register gives his mother as Elizabeth Dixon, ms Dixon
Henry's death certificate gives the mother as Agnes Dickson, ms Clark
James' marriage is old parish records with no parents recorded
David's job changes between agricultural labourer and miner between records, so it does give me pause, but I suppose he could have been a labourer in Ireland, and came to Scotland to work in the mines, as I know many people did.
Regarding the boys' mother, it seems likely that the mother was Elizabeth, possibly Clark, who died young and David remarried to Agnes, maiden name also Dickson, who became stepmother and gave birth to two half-sisters. The grandchildren didn't know the details of their paternal grandparents - as evidenced by Hugh's son not knowing their names, Henry's son mashing together Agnes with the surname Clark, and James' son giving the name as Mary Dickson.
Unfortunately I've not been able to find birth records for Henry, Hugh, or James, nor a death certificate for Elizabeth (if she exists). David and Agnes's marriage is an old parish record, with no detail as to whether he's a widower or not. Their marriage isn't until 1849, so I wonder if David, first wife, and three sons aren't actually living in Ireland in 1841, hence not finding them on the census.
Thanks for the help, everyone. While there's still some questions, I have more details than I thought I'd get, and have a theory I'm pretty happy with
