Hannah, I don't know of these people myself, but perhaps this may help?:
Dwelling: 8 Charles Street Census Place: Hartlepool, Durham, England Source: FHL Film 1342180PRO Ref RG11Piece 4908Folio 12Page 20
Marr Age Sex Birthplace George HOGGARTH M 26 M Hartlepool, Durham, England Rel: Head Occ: Revitter (Ships) Frances HOGGARTH M 28 F Blyth, Northumberland, England Rel: Wife James HOGGARTH 4 M Hartlepool, Durham, England Rel: Son
Taken from the 1881 Census - certainly sounds like your people?I know it doesn't mention your ggfather, but it seems to confirm the prescence of your gguncle James.