In 1851 we can see Sarah and 6 of her siblings at the Windsor Union Workhouse, Old Windsor.
Joseph Knibbs Pauper 15 Plasterer Hawke Boy Surrey Egham
John Knibbs Pauper 13 Shepherd Boy Surrey Bishopsgate Egham
Mary Ann Knibbs Pauper 8 Surrey Bishopsgate Egham
Sarah Knibbs Pauper 6 Surrey Bishopsgate Egham
Emily Knibbs Pauper 2 Surrey Bishopsgate Egham
Jemima Knibbs Pauper 4 Deserted Surrey Bishopsgate Egham
Frances Knibbs Pauper 3 Deserted Surrey Bishopsgate Egham
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The 1871 census shows Sarah living with her mother Mary Ann at Mile End Old Town, Tower Hamlets, Middlesex:
Mary Ann Knibbs Widow 54 Lodging House Keeper Bow Devonshire
Jemima Knibbs Daughter single 24 Machinist Egham Surrey
Sarah Knibbs Daughter single 28 Laundress Egham Surrey
Emily Knibbs Daughter single 8 Mile End Middlesex
Jemima Knibbs Niece single 4 Mile End Middlesex
Anna Farmer Lodger Widow 52 Silk Weaver Shoreditch Middlesex

We believe that Emily is the daughter Sarah.

Jemima is probably the daughter of Mary Ann's daughter, Frances Knibbs, so a grand-daughter rather than a niece as identified on the census return.
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I believe it was this Sarah Knibbs who died in Lambeth District, London, in q2/1873 which could account for why her daughter Emily went to live with Sarah's older Sister Elizabeth In America.