The last trace I have of this family is in Charlesworth, Derbyshire. I have the birth certificate of their son, also called Joseph Smith, born 10th October 1858 in Charlesworth, Derbyshire, at Higher Mill Lane. Father: Joseph Smith, Cotton Spinner and mother Jane Smith, formerly Greenwood.
He was baptised on 24th April 1859 in Charlesworth, Derbyshire, parents Joseph and Jane Smith.
On the 1861 census Joseph, the son, is age 2, living in Charlesworth, Derbyshire with his grandmother Fanny Greenwood, a widow, his aunt Mary, and Mary's son Henry Greenwood.
His mother Jane Greenwood was born July 1827 in Heptonstall, baptised 27th August 1827, Heptonstall. Her baptism record says she is seven weeks old at the time of her baptism, and gives abode as Manchester, even though the baptism takes place in Heptonstall. Her parents are Fanny and Henry Greenwood.
In 1841, Jane is living in Silk Street, Manchester, with her parents Henry and Fanny, and siblings.
Jane's marriage to Joseph Smith 2nd February 1851 at Manchester Cathedral. Witnesses are Mary Greenwood and Benjamin Smith. Both Jane and Joseph are living at 40 Beswick Street, Manchester, which is where Jane's mother Fanny and sister Mary are living on the 1851 census. Jane's father, Henry Greenwood, Overlooker (marriage document fails to note that he is deceased in 1851).
Joseph Smith, the father, born 1822 Heaton Norris, Lancashire. Birth place also given as Manchester on other documents.
The 1851 census shows Jane as wife, age 22, born Todmorden, with husband Joseph Smith age 30, born Stockport, Cheshire, and his son William Smith age 8, born Stockport, Cheshire. Jane is a Cotton Bobbin Frame Tenter, and Joseph is a Cotton Spinner (this occupation same as on son Joseph's birth certificate). Abode: Tonge Street, Manchester.
After the 1858 birth of son Joseph, and his mention on the 1861 census living with his grandmother Fanny in Charlesworth, I can find nothing about this family. Ancestry is giving hints about a Jane Rose, but I can't find any death record for her husband Joseph Smith.