Hi Matthew
This really is a puzzle which is why I am looking at all angels in the hope that something will drop into place.
I'm amazed that we can't find any of them in 1891 or 1901, I still haven't found Ernest/Alfred in 1901. I think you are right in thinking they all hid from the census enumerator.
The only possible sighting of William Carter & wife Charlotte in 1891 is the one I spoke of before although their names are wrong but ages & birth places are near enough.
George W Carter aged 74 born London Islington
Emma Carter aged 59 born Sheringham Norfolk (a stones throw from Cromer)
H Carter daughter aged 19 born Herts (just an initial no first name)
They are living at White Lodge Terrace Barnes Surrey & Barnes is where William died, Charlotte is with her daughter Jessie in 1901 in Barnes, a widow.
I also cannot find a marriage for William & Charlotte but did they ever marry, is that perhaps why all the children have the Curtis name as well as Carter. As William was born in 1818 he could well have been married before he met Charlotte & they had Jessie in 1855.
There is a marriage record on Free BMD in June qtr 1857 St Giles that does include a Charlotte Curtis & a JAMES Carter but unfortunately I can only find it on Free BMD, nothing on Ancestry to see which groom married which bride. Strange thing is William is William J Carter on the 1871 in Harpenden.
I don't know if Charlotte's death cert will help in any of this but I'm sure it's worth getting if only to find where she was & perhaps why.
I am puzzled over the fact that Harry was asked if he wanted to go live with his father before Charlotte married Ernest/Alfred, that is strange. Obviously Charlotte was never married to George Williams or the boys would have that surname which is another odd aspect with George being an Anglican Vicar surely he would not be living with someone who wasn't his wife or not be married to the mother of his children, unless there was a reason that prevented this happening.
All very peculiar but intriguing. There must be an answer out there somewhere.
Maddie