Son John was found under mother's name of Rachel Nicolson.

I have found this family in the 1861 census living at Rubislaw, Whitehouse in Old Machar. Husband John is not included but Rachel is described as "Blacksmiths wife" not widow.

I found the record of daughter Rachel's death on the FamilySearch website

The entry for this family in the 1851 census has a very strange entry for a five year old son which looks like the name has been modified. I believe this is really a daughter "Jane".

Daphne Maddox has sent details of her research into John's parents:

O.P.R. Births. ScotlandsPeople (www.scotlandspeople.gov.uk). Original record: 222/00 0010 0203, Old Parish Registers -- Births. Midmar (Aberdeenshire, Scotland), National Records of Scotland, Edinburgh, Scotland. "26th May: Robt Mutch + his wife in Tillyronach had a son named John

She has also sent a link with fuller details of her connection to this family line through son William. You can view these at her page on WIKITREE.

Carol Doyle has provided the following details of her family which links to the known information about this family:

I know from what my Great Grandmother Jane Mutch and her sister Aunt Rachel Mutch told my Grandfather Charles and my Mother Muriel when she was young was some of the family fought as Jacobites in some of the uprisings in Scotland.

Rachel and Jane's brother was called either Robert William Mutch or William Robert Mutch not sure which way it was but he left Scotland for USA and settled in Cleveland, Ohio and married someone there and they had five daughters and only one married and the rest had professional jobs after finishing college and university in the USA.

They had a cousin named James Mutch who left Scotland for USA and he settled and married in Rochester, New York State, USA ......

...... I am the Granddaughter of Jane Mutch Gates. When she came off the boats in either Quebec city or Montreal my Great Grandfather George Alfred Gates met her and courted her at that time and they married in Pittsburg Township, just 3 miles outside of Kingston, Ontario. Pittsburg township is East of Kingston, Ontario.

Her sister came out to Canada after their parents died in, I think, late 1800's or early 1900's and she also settled in Pittsburg Township and she had never married - that is Rachel Mutch my Aunt. They lived on my Great Grandfather's farm (George Alfred Gates) and Aunt Rachel did the cooking for the family as Jane Mutch Gates had 3 sons.

One son was my Grandfather, Charles Nicol Gates born in Pittsburg Township and he married Agnes Elizabeth Seale Gates. They had one daughter Muriel Isobel Gates my Mother who married James Mercer Harper - he was born in an Edinburgh Hospital and brought up in the Balerno and Currie areas of Scotland south of Edinburgh. All the Harpers and Falconers part of my family were from Balerno and Currie Areas of Scotland. My grandmother Jean Mercer Harper was born Mercer and her family were from Leeds [sic: Leith?] across from Edinburgh near the sea coast looking towards Europe.