What a tangled web! However, I agree that that Jane is a second wife and have found the following:
William Green, widower, Hawker, son of George Green, Hairdresser married Jane Griffiths, widow, dau. of Joseph Law, Fishmonger on 25/1/1863 St. Lukes, Middlesex - the address for both is given as 'White Cross' which ties in with the address on 1871 Census.
Therefore, I would say the 1871 Census details you have for Sarah with William and Jane is spot on.
The Sarah with Thomas and Susan Turpin is in 1861, not 1871, and she is shown as aged 8. Thomas and Susan - per 1851 Census, ref.HO107 - 1542 (or 1842, can't read my own writing) - 398 - 32, had a dau. Sarah bc.1834 - she may be the Sarah Turpin married to William Green and thus Sarah Green was actually their grand-daughter.
Have found a record of the marriage of William Green and Sarah Turpin in familysearch but only the bare details given: married 18/7/1852 St. Thomas, Stepney.
Although I can't find them on 1861 Census, an Oscar Griffiths birth is recorded in the Dec.qtr.1857 Shoreditch which fits with him being Jane's son.
So, sometime between Sarah's birth in 1852 and 1863, Sarah Green, nee Turpin, died and young Sarah lived with Thomas and Susan Turpin, who were either her grandparents or some other relative.
As the meerkats would say 'Simples'!
Annette