I can't give you the answers, but this would be the best starting point (BDM's and Censuses). That's where I got all my Scottish history from. Forgot to mention, there are fees, but I found them reasonable.
The 1841 census from Ancestry.co.uk: living at Birtwhistle Street, Kircudbrightshire Hugh Henney (maybe should be Hannay?) 50 cotton HLW born Ireland Mary Woodside 25 William Woodside 20 cotton HLW
Don't know if this is your family as Mary should be Margaret, and William's occupation is wrong, but the Henney/ looks promising and they may fit in somewhere.
The IGI has an extracted entry for AGNES WOODSIDE, b.12 FEB 1843 Girthon, Kirkcudbright. parents WILLIAM WOODSIDE and MARGARET KENNEY.
Given the timeframe and locality it seems likely that this is your family, but may just be another mistranscription of the surname.
Have you tried to find death certificates for either of them? They usually give some information as to date of birth or parents if these were known by the informant.