I don't understand how you are jumping about with different names, etc. Let's start at the beginning.
Rosie17 has posted lots of information from certificates NOT muddled family trees.
Your great-grandmother:
Annie Christie, born 18 December 1869 Govan Lanarkshire
Father James Christie, Mother Elizabeth Devlin
Also on the certificate- "parents married 1868 Ireland"
Then, "According to marriage certificate for Annie Christie both parents were deceased 1914" and "Occupation of her father on her marriage and death certificates he is a gas work labourer Stoker."
So, have you found Annie Christie in all possible census records to check family details? I would expect she might be in 1871, 1881, 1891, 1901 & 1911 before her marriage. Depending on how much before 1914 parents died you might also find them with Annie in many of those records. If the parents married in Ireland they might easily have been born in Ireland and having a more exact location should help when you are ready to search Irish records- the 1911 census is one most likely to record a more exact place of birth than 'Ireland' but you need to follow up every record.
Finding parents in census records will then narrow down when they died so you can then look up death certificates on Scotland's People (not what is on someone else's tree). Death certificates should list names of both parents so you can see if they died in Scotland or Ireland.
It is consuming but you need to trace all possible Scottish records since you don't have a location and marriage hasn't easily been found in Irish records.
