Linda,
I searched the Irish Catholic marriage and baptism records on Ancestry for Owen & Mary’s marriage and the baptism of their children but without success. Not every parish has records for the years you need and that may be the explanation.
I can tell you that the family’s move to Scotland was probably around 1849/50. They are in the 1851 Scottish census (as McShary) for Duntocher in Dunbartonshire. Daughter Mary was 3 then and born in Ireland.
You are a bit unlucky. In 1855 (first year of statutory birth registration in Scotland) and from 1861 onwards, Scottish birth certificates record where and when the parents had married. Owen & Mary had a son Andrew McSharry born in 1856, but I don’t see any more children after that, so you just miss out on that vital information. The family were still in Duntocher in 1861. (Owen seems to have changed his name to John).
Can’t immediately see their death certificates but if you find them, Scottish death certificates should contain the deceased’s parents names and occupations.
Regarding Hugh Moore, do you know what denomination he was? Looking at the 1901 Irish census, the majority of women named Susan(na) were Church of Ireland or Presbyterian. Were these Moores Protestant? If so, many of those records for the 1830s are not on-line, plus as with Catholic records not every church has records for that period, and without some idea of where he came from it’s a needle in a haystack.
However, the 1872 Scottish death certificate should record whether Hugh’s parents were alive at that date. If dead it will say (dcd) or deceased after their names. If still alive, it will show nothing. It should also record Hugh’s father’s occupation. If you let me know whether Hugh & Susanna were still alive in 1872 and Hugh senior’s occupation, I’ll see if I can find anything more in Ireland.