In household of John W and Sarah A Hamilton:
brother-in-law: John G Dixon, age 33, born in Kendal, Westmorland, blacksmith's stocker labourer
sister: Ann E Dixon, age 33, born in Barrow, Lancs
niece: Amy E. C. Dixon, age 11, born in Barrow, Lancs
nephew: Thomas Dixon, age 9, born in Barrow, Lancs
nephew, John G Dixon, age 6, born in Barrow, Lancs
niece: Sarah A Dixon, age 1 mo., born in Barrow, Lancs
It is possible that Ann E (born in Barrow, Lancs) is the same person as Amy E (born in Dudley, Staffordshire) in the previous census (since census records are not always accurate). It is also possible that this is a second wife, especially given the gap in ages of the children.