Here is the 1851 census
John Moxon, head, age 33, oil mill lab born Morton Lincs
Susannah Moxon, wife, age 33 born Waddingham Lincs
Fanny Moxon, daughter, age 7 born Gainsborough Lincs
Charles Moxon, son, age 1 born Gainsborough Lincs
HO 107 2120
folio 162 page 16
Gainsborough, Lincs
In 1861 Fanny was a 17 year old servant away from home.
I cant see Charles in 1861 but here are the parents
John Moxon, age 44, labourer born Morton
Susanna Moxon, age 43 born Waddingham
George Moxon, son, age 9, scholar born Gainsboro
RG9 2409
folio 25 page 16
Gainsborough, Lincs
I have the 1871 for the parents and George if you want it. I will see if I can find Fanny or a marriage for her.
Nicky