As a widower Samuel Ellison married Jane Forth (widow, nee Hopwood) on 4 Sep 1859 in York.
1861 census has the family living at 59 Laurence St, York.
Samuel Ellison, married 35, farm labourer, born Heslington Yorks
Jane Ellison wife, 30 dressmaker born Upper Helmsley
Harriet Ellison, daughter, 9 scholar born York
Samuel Ellison son age 1 born York
Elizabeth Forth daughter age 8 born Acaster
Thomas Forth son age 5 born Gate Fulford
Baptisms for Samuel (13 March 1826) and Isabella (2 July 1823) both in Heslington confirm they were siblings.
I can´t read my own handwriting! The 1861 census said Harriet was born in Heslington. That ties in with the burial for her mother Isabella, the record says she was aged 27 and of Heslington. I think Dave is right, Harriet moved to Sheffield after the death of her father and was taken in by her aunt.
In the 1871 census, Harriet was working as a general domestic servant for a Mrs Wilkin at 57 Monmouth St. She was still going by the name of Ellison then.
Despite what the 1861 census says, Harriet was not yet 8 yrs old at the 1861 census and at the times of the 2 marriages she was not yet 18. Note that the first (jncorrect) marriage was just 8 daysafter the 1871census, so she knew her name was Ellison
I wonder if she was confused by the fact that her real mother was Isabella and her aunt was also isabella. And maybe at the time of the first marriage she did not know her real father name so she used Thomas Richardson. Once the error was realised the only way to put it right would be to have a second marriage with the correct names
Dave