The 1861 census transcription at FreeCEN lists in the poor house in Old Machar Peter Copland, 80, widowed, formerly quarrier, born Rothes, so it looks as if he did not die in 1852. I recommend a look at that 1862 death certificate.
He is also in the 1841 census in Woodside, aged 55, quarrier, born outside the county, with Helen Copland, 50, born Aberdeenshire.
As he was a pauper, there will be information about him in the Aberdeen parochial board records. He will have applied to them for relief and they will have dealt with him. One of the things routinely asked of applicants was the names of their parents. Depending on how long he had lived in Aberdeen, they may have written to Rothes to claim back the cost of looking after him.
I note the baptism of Patrick Copland, son of William Copland, baptised in Rothes on 15 September 1781. The names Peter and Patrick are used interchangeably, so this is probably him. There are seven more baptisms of children to Wil/l/iam C*p*land in Rothes between 1754 and 1779, but no obvious marriage. However at this time the Rothes baptism records often contain useful details about witnesses to baptisms, sometimes describing the relationship of a witness to the child, and one can sometimes deduce the name of a missing mother from these.
I see that the eldest son of Peter Copland and Isabel Shand was named William.