When trying to find the mother's LNAB - last name at birth - try looking up the children's birth registration at the GRO (General Register Office). A birth registration should show the mother's maiden name.
Registration started in 1837: I couldn't find George's birth in any district near Croydon. That may be because he was actually born before registration started. The other children were born before 1837, so no joy there.
There are 1871 & 1881 census records for George Stevenson, born 1838 Croydon, in Woolwich. He is head of the household, has a wife and children.
I would be careful relying on Family Search records - accuracy can vary!
Happy to help more if you get stuck :)