Tiffaney
I'm a bit stuck here too! From FreeCen 1841, I cannot see any Sutherland family groups with a William and Christina (and variants) who have a child Christina in the household. There are some entries where there is a William father but mother's name is different and vice versa (as I'm sure you have found when you have gone throught it).
Were these parents' names also on Christina's NZ marriage cert.? Sometimes, depending on the informant, the information given when reporting deaths can be incorrect (children may not remember the names of their g/parents).
I've had a quick look on Scotlands People, the official Scottish pay to view BMD and Census site. There are no death entries coming up for a female (any first name) Sutherland, other name Sutherland, any age, anywhere in Scotland between 1855-1955. Official Registration began in Scotland in 1855, so it could be that Christina's mother died before this date and no on-line record exists.
In which case, you are back to the censuses. Certainly if the family remained in Caithness, at least in 1841, there is no record of them with those parents' names. I would open up your birth years for Christina, if she died in 1912 aged 76, then her birth year would be c.1835-36. The IGI submitted entry may just be a little bit of a 'red herring'.
Monica