Are these the illegitimate children of our Charles Duncan Jr. born 1835? Charles Duncan was about 33 if he fathered a child also known as Charles. Charles Duncan, Christinas brother. This is where he may have met Jessie if she was related to Dr Pirie and was visiting him at Dundee or else Charles Duncan sailed boats to Aberdeen. He may never have married Jessie Pirie. Jessie was born in 1843 in Ellon. Charles could have been on a voyage and met Jessie and had two children. Ellon where Jessie grew up is 16 miles north of Aberdeen where Charles could have been on a ship.
Also Charle's parents had an illegitimate child so he may have become used to the idea as being okay.
Charles is not mentioned as the father, only as the son. And why is the family living in the police station in the 1871 census? Jessie is a dress maker and her father is a mason’s laborer.
In the 1901 census in Ellon Jessie is living with her mother Catherine, no profession. Jessie is a dressmaker on her own account at home and her daughter Catherine Duncan is a milliner.
I noticed in census that Jessie was still a scholar at 16. This is unusual as normally would be sent out as s servant to help make ends meet. I would say that is highly educated for the day.