Joseph can be seen in 1871 census living at the address of Olney, Silverstone, Northamptonshire, England:
Thos. Knibbs 55 Labourer Oxon, Deddington
Sarah Knibbs 56 Oxon, Adderbury
Phoebe Knibbs 25 No Occupation Oxon, Deddington
Jos'h Knibbs 22 Labourer Oxon, Deddington
Their address was 'Olney, Silverstone, Northants'

The census was taken on 2nd April 1871, so at the time of the census, Joseph's first wife Elizabeth was still living. It appears that at the time he had his parents and sister staying with him in Silverstone, so I assume his wife was ill in hospital? No sign of the son either.
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Joseph appears in the 1881 census living at 435 Manchester Road, London, England.
Joseph KNIBBS Head M Male 30 Deddington, Oxford, England Gen Lab
Harriett KNIBBS Wife M Female 27 Buckingham, England
Joseph W. KNIBBS Son Male 6 Birmingham Scholar
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Joseph appears in the 1891 census living at what looks like 11 Glew Terrace, Poplar, London:
Joseph Knibbs Head M 41 Storekeeper Engineers Yard Deddington Oxon
Harriett Wife 38 Buckingham Bucks
Joseph W Knibbs Son 16 Chipper Ship & Bridge Building Yard Birmingham Warwick
Charles F J Knibbs Son 3 Poplar London

also,

Name Relationship Age Gender Birthplace
Joseph Knibbs Head 41 Male Deddington, Oxfordshire / Oxon
Harriett Knibbs Wife 38 Female Buckenham, Buckinghamshire
Joseph W Knibbs Son 16 Male Birmingham, Warwickshire
Charles F J Knibbs Son 3 Male Poplar, London
Town: Tower Hamlet, Ecc. Parish: St John, Civil Parish: Poplar, County: London
Registration: Poplar, Poplar, 34
Source: PRO/National Archives Reference # RG12/336 Folio 55 Page 41
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Joseph appears in the 1901 census aged 50, living at Manchester Road, Poplar, London with his second wife Harriett (47) and children Chas (13) and Dorothy (3). All four are listed under NIBBS in the 1901 census.
Joseph Nibbs 50 Oxford Deddington Labourer In Ship Yard
Harriett Nibbs 47 Buckingham  
Chas Nibbs 13 Poplar London
Dorothy Nibbs 3 Poplar London

Also living with them were two nieces May Bunting 10, and Lilly Bunting 9, also from Poplar. 
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We see Joseph in 1911 living at 581 Manchester Road, Poplar, London with his wife and son Charles:
Joseph Knibbs Head Married M 63 Dock Labourer Oxon Deddington
Harriet Knibbs Wife Married (37 years) F 58 Bucks Buckingham
Charles Knibbs Sin Single M 23 Dock Clerk Poplar London
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June Knibbs shared the story of her great-grandfather Joseph, who, on his travels to London from the Banbury area (Deddington?) stopped at a farm and fell in love with a young girl there, and took her to London. This story is reminisced to the family by her somewhat romantically minded Uncle Leslie, Joseph's grandson.