I think I've possibly found Charlotte with the two oldest children in 1861:
RG09/2434/45 /22
30 Holden Square, Greasley, NottsAaron CARY Head 27 Coal Miner b. Ripley, Derbyshire
Charlotte CARY Wife 23 b. Belper, Derbyshire
William CARY Son 3 b. Oldhill, Staffordshire
Francis CARY Son 1 b. Greasley
Aaron is on the 1841 and 1851 censuses with his parents in Ripley, when the surname is given as KERRY, and his death registration is also under KERRY in 1880.
However, I can't spot him in 1871, and I can't see a marriage to Charlotte...

As Aaron didn't die until 1880, it looks as though he and Charlotte separated prior to 1871.
There are possible birth registrations for all the older children as KERRY, but Absolom's birth seems to be registered both under SWAIN and KELLEY.
Rambler