Wife Anne in 1851 replaces Nancy, who was present in 1841. The gap in the births of the children suggests they married about 1842-46, but only Marriage near Bolton St. Helens or Wigan is for Mary Rogers, which seems a little early, but possible.
Ann on 1851 and 1861 census, Anne 1871.
There's an Anne Barrow living with Son-in-law Joseph and Daughter Sarah Ann Flocton in Hulme, Lancashire in 1881. If this is right, then Ann must have had this daughter from an earlier marriage.