Hi Jackie - now it's gone a bit quiet after Christmas, there is time to catch up on some delving!
By 1911, that John had moved to 27 Bond St Northam. Harriet and Annie are still with him and another son Sidney born 1905. He is recorded as a Widower, married 20 years having had 10 children - 7 of whom are still alive. Mary is possibly the one who died 1st qr 1909 South Stoneham aged 44 but I would have expected "Southampton" rather than "South Stoneham". Florence is not with them and hence may be the one at the Princess Louise Home for Girls at Kingston Surrey.
However, on the 1901 census, there is another Florence Cox in Southampton of the same age also daughter of a John and Mary Cox but with siblings Walter,Sue and Maud ( by 1911 that Mary has also died and Reg, William and Nellie have come along)
You sound pretty sure but before going further with either line, could you confirm that Florence's siblings you mention are from "Family Memory" rather than an initial look at the 1901 census - I don't want to mislead you by chasing the wrong family !
Regards Derek