Just a thought but if she is still living in Manchester in 1851 its very possible she may be living in one of the districts where the records didnt survive.
There are some good kind souls on Rootschat who have access though to the 1851 unfilmed cencus records for certain parts of Manchester so maybe you could try a new topic specifically asking for a look up of the unfilmed records
Jane
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Kershaw, Longbottom,Parvin Areas Huddersfield, Brighouse, Rastrick ,Thirsk, Sand Hutton Masters in London/Surrey Cencus information is crown copyright from www.nationalarchives.gov.uk
Not sure if you have access to cencus but in 61 she was living with her sister if you need details i will post in a couple of minutes
Jane
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Kershaw, Longbottom,Parvin Areas Huddersfield, Brighouse, Rastrick ,Thirsk, Sand Hutton Masters in London/Surrey Cencus information is crown copyright from www.nationalarchives.gov.uk
Sorry I was on the phone.....again and apologies I meant to say living with her brother
1861 Cencus-Sandbach RG9/2614/38/32 Elworth St
William Rhodes 41 head b Tintwistle Ind Minister of Hope Chapel Margaret " 41 wife b Liverpool Sarah " 36 Sister b Tintwistle Visiting Emma Mainwaring 20 b Sandbach House Cook Esther " 15 b " House Maid
Jane
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Kershaw, Longbottom,Parvin Areas Huddersfield, Brighouse, Rastrick ,Thirsk, Sand Hutton Masters in London/Surrey Cencus information is crown copyright from www.nationalarchives.gov.uk