Emma Green born 1854 was in fact named Bate the daughter of William Green and Harriet Bate who it appears never married.
1871 Long Lane ,Hill,Worcs
William Green age 61 labourer b. halesowen
Harriet Green age 59 Housekeeper born Clent
Twins Charles and John Green age 19
Emma Green 17 Nail maker
Ephraim age 15
Harriet age 11
Polly Bate age 5 grandaughter
1861
Carters Lane ,Lapal
William Green age 51 widower b. Halesowen
Harriet Bate unmarried age 43 housekeeper
Thomas Green age 21
Mary Bate age 16
John Bate age 12
Charles age 10
Emma age 7
Ephraim age 4
Eliza age 2
sarah age 10 months
1851 Carters Lane
William Green age 41 widower
William Green age 16 son
Ann Green age 13 daughter
Thomas Green age 10 son
Harriet Bate age 29 housekeeper
Mary ann bate age 6 lodger
James Bate age 2 son born out of wedlock(this is on the original record)
Charles Green Bate age 1 week ,son
John Green Bate age 1 week,son