think the one born 1876 is with his brother william born 1874 in 1901
so going by your opening post where you say the childrens names as james,joseph,jane,mary.
it would be the other james born c 1874 who would be more of a possibility
here he is in 1901
RG13/4002/23/16.
james hodgson age 27. b. liverpool. occ. thread bottom turner. head
elizabeth.e. age 27. b. finssthwaite,lancs. wife.
ernest age 4. b. ditto. son
lily age 2. b. ditto. daughter.
bessie jenkinson age 11. b. ditto. step sister in law.
living at; colton,lancs
reg.dist. ulverston
of course this is only guesswork you would need this couples marr cert to be sure this is the right james