hi lisa, I have found what looks like your family in the 1871 census and the 1881 census.
The 1871 census contains a record of an Elizabeth age 45, with the three named children, aged 17, 12, and 10 respectively. There is no husband Charles or Frederick in the list and they are in the Camberwell district. (I did not pay to view the whole record)
The 1881 census lists them at 3 Pinnocks Place Camberwell, Surrey: Elizabeth is widowed (aged 50), daughter is not there (possibly married and living elsewhere), sons occupations are both coal porters and they are living with a neice and two nephews, surname Davis, and two lodgers.
If you view the full records maybe Elizabeth was widowed in the 1871 census also. I couldn't find a death record for Charles between 1861 and 1871. If you can't find it, I suppose it might be worth checking to see if he was killed overseas in one of the Victorian wars. My great grandfather who also lived in Camberwell was in Burma during the 1881 census, but I had no way of knowing this until I found his army papers which contained a list of all his locations during his time in the army. It also gave the names of siblings.
good luck with your searching, hope you find what you are looking for,
jenny