Thank you for giving details of the 1873 marriage - however, as you confirm John's father was indeed John Carey, deceased, why were you thinking he was the son of James and Emma?? Would seem that James and John were brothers:
John Carey bp.15/4/1821 Rochford, Essex, son of John and Mary Ann
James Ellis Carey bp.3/11/1822 Rochford, Essex, son of John Ellis and Mary
John Carey bc.1798 buried 20/12/1833 Barling, Essex
Widow Mary Carey remarried to William Ellis 22/9/1838 Barling - he single, she a widow, both of full age, his father Martin Ellis, Labourer and her father Samuel White, servant.
Could not find online a marriage for John Carey and Mary but from the above her maiden name was White - she and William Ellis had a daughter Mary in Dec.qtr.1839 Rochford, mmn White.
From 1841 and 1851 census it would seem that besides sons John and James Ellis, John and Mary had at least 2 other children:
Samuel Ellis Carey bp.26/2/1826 Barling, dau. of John and Mary (surname listed as Kerry).
Catherine Ellis Carey bp.18/5/1834 Barling, dau. of John and Mary.
John Carey and Mary White must have married ca.1820 but can't find the marriage online.
John Carey was bc.1798 (place not known) and Mary White bc.1800 Thundersley, Essex (per 1851 census but cannot find baptism for her there).
Hope this helps.
Annette