Hate to disappoint you but in 1851, Sarah Hoskin was described as the Head of the household but also as a wife. She had James, mary and Josiah but plainly her husband, if she was actually married, was away from home. sarah was on King Street, Stoke Damerel.
You may have to get one of the childrens' birth certificates to find out who the father was.
Cheers,
Jen