Hi Craftycorner,
I hope to help with this one as my surname is Attwater. This family can be found on the 1841 census at:
HO107/29/10, Folio 7, Page 35 and HO107/29/10, Folio 8, Page 36
District: Wokingham, Sub-District: Wokingham
Lambeth Hill, Shinfield, Berkshire
Missing from the 1851 census are Lucy age 11, William age 9, Sarah age 7 and Susannah age 4.
Lucy can be found in the 1851 census at:
HO107/1681, Folio 177, Page 1, Household 2
District: Basingstoke, Sub-District: Basingstoke
Church Street, Basingstoke, Basingstoke, Hampshire
She is a general servant. Ages are not given for the deaths at this point in history but it looks like William died in 1850. He would have been about 18. Sarah would have been about 17 during the 1851 census and is a possibility of being the mother?
The mother Louisa (who by the way is listed as Lucy in 1841) looks like she died in 1860. Daughter Lucy looks like she may have come back home to help her father. It is quite possible that all three grand children are hers.
The only way to be sure at this point is to order the birth certificate.
I hope that this has been useful and hasen't confused you research further.
Nancy