I think Joyce here is a daughter born to Caroline out of wedlock, father unknown, and is a HILL rather than a WHILE:
http://bcconnections.tribalpages.com/tribe/browse?userid=bcconnections&view=0&pid=20571&rand=1461048
1871 Siviters Lane, Rowley Regis
James Whitehall Head 40 Miner
Catherine Whitehall Wife 32 Nailer
Jocie Hill Daur-in-law 15 Nailer
Patience While Daur-in-law 12 Nailer
Eliza Whitehall Daur 1 month
All born Rowley Regis
It seems in same building:
A family of Westwoods,
then:
Elizabeth Hill Head (Lodger crossed out) Widow 54 Nailer (Caroline's mother)
Sarah Jane Hill Daur 19 Nailer
Amelia Hill Daur 15 Nailer
All born Rowley Regis
I also think that Joyce had a son, Joseph, out of wedlock prior to her marriage to Thomas Southall.
1881 5 Siviters Lane, Rowley Regis
Caroline Whitehall Head Widow 41 Nail Maker
Joyce Southall Daur Mar 24 Nail Maker
Patience While Daur Unm 22 Nail Maker
Eliza Whitehall Daur 11 Scholar
John Fredrick Whitehall Son 6 Scholar
Thomas Southall Son-in-law Mar 25 Bricklayer's Labourer
Joseph Hill Grandson 6 Scholar
Kate Southall Granddaur 4 Scholar
Samuel Southall Grandson 2
All born Rowley Regis
What do you think?
(PS. Caroline's 1st husband should be Joseph rather than James?)