The 1881 Household (which you already have) has Richard Pendlebury as a Cotton Dyer born Lancashire, Ratcliffe, as well as his wife Sarah and the children Richard and Elizabeth all born in Lancashire there are two other children:
William Pendlebury, born "Hill Top" Lancashire, aged 14
John Thomas Pendlebury, born New York, America, aged 13
This is what I found in 1871.
4 Manfields Place, Pendleton, Salford
The head of the houseold was John Denson, wife Ann Denson also born Ratcliffe/Radcliffe (possibly a sister of Richard Pendlebury?)
Richard Pendlebury, boarder, married, Dyer, aged 36, born Ratcliffe/Radcliffe, Lancashire
William Pendlebury, boarder, aged 5 born America, (British Sub)
Thomas Pendlebury, boarder,aged 3, born America (British Sub)
Not an exact match as in 1881 and 1891 William's birthplace is given as Lancashire, but as there is a 13 year old John Thomas born in America in the 1881 household and as Richard Pendlebury's occupation, age and place of birth all matches I think it is the same people as in 1881 and 1891.
I haven't been able to find Sarah Pendlebury in 1871, of course the other children were not yet born then, but as there was a 5 year gap between John Thomas/Thomas and Richard I wonder if Sarah was Richards 2nd wife?