Joseph had died by 1861 census.
Living with his widow Jane at Atheneum St., Bishopwearmouth, and children is :
Mary Duxfield, 49, sister in law, unmarried, Grocer, b. Northumberland, Mindrum (? its very blurred) Northumberland.
In 1851 census there is a Mary Duxfield living at Walker Station, Longbenton, Head, 39, unmarried, Keeper of Grocery Shop, b. ******, Northumberland. Could be Mindrum.
Can't find her in 1841 or 1871.
Another route to finding Josephs parents.
Alan.