Hi again, Isabella could have been the illgitimate child of Jane who would have been aged 21 at her birth. When Jane married James accepted Isabella into his family by using his surname.
Do you know when James & Jane married? Probably c. 1855 given the age of Joseph unless they had earlier children who died. Have you their marriage cert? That would give Jane's name before marriage to James, and tell you if she was a widow or spinster. the you could search for Isabella's birth and see if she was Jane's daughter.
The thing that raises a red flag is the order of the kids in the census. I gather from what you give as the census info, no relationship to head of house is stated? Is that correct?

charlotte