You are never going to locate Elizabeth Chapman's death certificate because death certificates did not exist before 1855.
All you really know about Elizabeth or Betty Chapman is that she was born in Durris in about 1825/1826, had a daughter Margaret Wright in 1845/1846, married John Niven/Nivens on 5 December 1817 in Durris and had three more children
Christina born 16 May baptised 31 May 1849 in Durris
John, born 26 February baptised 2 April 1851, Banchory-Ternan
William, born 23 January baptised 26 January 1853, Banchory-Ternan
and died before 31 July 1855, when her widower remarried.
There is only one baptism of an Elizabeth Chapman in Kincardineshire between 1824 and 1826, the daughter of Charles Chapman and Mary Wood, baptised in Fetteresso (the parish in which Stonehaven is situated) in July 1826.
There are two Elizabeth Chapmans in Kincardineshire in the 1841 census. One is the above, living with her parents and siblings in Stonehaven. You can eliminate her. She married Alexander Stephen in Fetteresso in 1850, had eight children, and died in Fetteresso in 1906.
That leaves another who is a 14-year-old servant in the household of Robert Lawson, blacksmith, at Mains of Brotherton in Benholm. There is nothing to show that this is your Elizabeth/Betty, however. There are no Chapmans in Durris, and no others in Benholm.
As others have pointed out above, John and Elizabeth/Betty's children were with their
paternal grandmother in the 1851 census.
this information I got from the birth of an Illegitimate child Margaret Wright b 1846
What information did you get from this birth? And given that it isn't on Scotland's People, where did you get it? And what exactly does it tell you?