If you study the children with James and Frances you will find from baptisms on familysearch that Frances was not the mother of the children - Frances was a second wife:
James Nye, widower, son of Abel Nye, married Frances Vowell, widow, dau. of Christopher Woodington, 8/7/1839 St. Marys, Chatham.
James's first wife was named Elizabeth and think this is probably the marriage:
James Nye married Elizabeth Tomlin 7/4/1811 Aylesford, Kent.
James and Elizabeth had the following children baptised (which includes 4 who are not on the 1841 census in Gillingham):
Sarah Ann b.13/11/1811, bp.18/5/1812 Wesleyan at either Tunbridge Wells, Maidstone or Sevenoaks (all 3 shown on familysearch)
Henry Joseph b.26/2/1813, bp.6/10/1813 ditto
James bp.11/9/1814 St. Margaret, Rochester
William bp.12/4/1818 St. Mary, Chatham
Marianne bp.28/11/1821 ditto
Thomas bp.4/5/1823 ditto
Eliza bp.20/6/1825 ditto
John bp.28/12/1828 ditto
Abel Robert bp.25/12/1831 ditto
Rachel bp.7/9/1834 ditto
1st wife Elizabeth bur.15/11/1834 St. Mary, Chatham aged 44 years.
So, all in all, the online trees referred to are somewhat 'up the pole' i.e. Frances was his second wife and not the mother of James' children, his first wife and mother of children is Elizabeth, AND as his second marriage details show, James was son of Abel (baptism details as posted by bearkat). James' mother was therefore not named Ann Rippon. As you've found yourself, the online trees omit specific details and looks like people have 'guessed' and others have blindly copied wrong information.
Abel Nye, bachelor of Chatham, married Mary Kitchingham, spinster of Newington, 13/9/1777 Newington, Kent after banns (per Kent Marriages).
Annette