Can't find Henry and Mary Gemmell in the 1871 census but their daughter Helen ( age 3) is with her paternal grandparents John and Helen Murphy living at Gowkhill, Holytown, Bothwell. She is very badly transcribed on the various indices so not easy to pinpoint.
Scotland's people have her as Helen Gemmill age 3( ref 625/2 5/35). John ( age 50) and Helen ( age 44) Murphy plus their son Thomas ( age 12) appear on the previous page ( ref 625/2 5/34). Findmypast have her as Helen Gernmill, granddaughter age 3 born Ireland ( I think this is a mistake - see later). John Murphy is age 50 born Ireland, a Pit Labourer, Helen Murphy is age 44 born Ireland and their son Thomas is age 12 ( shown as born Bothwell but their is no obvious birth for him and in the 1881 census he is still living with his parents and place of birth is given as Ireland. I think the places of birth for Thomas Murphy and Helen Gemmel may have been accidentally transposed in 1871).
Ancestry have made a real hash of this entry. John Murphy is age 50 born Ireland but Helen is mistranscribed as Helne and her age is given as 46. Thomas is correctly described as age 12 born Bothwell. Helen Gemmell is transcribed as Peter Gemmiill !! age 2 born Ireland.
In 1881 John and Helen Murphy are living at North Road, Holytown. John is age 60, born Ireland, a Coal Miner and Ellen is age 55 born Ireland. Thomas is still with them, age 23, now shown as born Ireland. Also in the household is Thomas Gemmel age 12, grandson, born Newarthill, Lanarkshire ( I think this is Henry and Mary's son John Thomas, born 1869).
I am not sure where you got Edinburgh as a place of birth for Mary. Was it a census? If Mary was the daughter of John and Helen Murphy above then I think it is much more likely that she was born in Ireland as the family still appear to have been living there as late as 1859 when Their son Thomas was born.
Isobel