This is a strange one living Skerton, Lancaster in 1871 
RG10/4230 f32 p26
Rebeca   Varey   60   born   Barwick... ?? occ Hawker
John   Lawther   Son-In-Law 22   bn Ulverstone occ General Dealer
Margaret   Lawther   Daughter   22   bn Althaw ? Moor
Robert   Lawther   Son-In-Law's brother   11   bn Ulverstone
.......
Rebecca/William Veary living Gt Bolton in 1851
William   Varey   33   Hawker Carpets   bn Not known
Rebeccah   Varey   35   bn Not Known
Rebeccah   12 bn St Helens, Lancashire
Grace   8 bn Gt Bolton
Margaret 2   bn Halshaw Moor 
HO107/2211 f24 p40
ADDED probable death
Deaths Mar 1880  
VAREY    Rebecca    68    Lancaster    8e   484
Lancashire OPC
Baptism: 27 Oct 1844 St Paul, Blackburn, Lancashire, England
Grace Varay - [Child] of William Varay & Rebecca
    Born: 15 Oct 1844
    Abode: Blackburn
    Occupation: Potter
    Baptised by: A. G. Edouart
Baptism: 11 Feb 1849 St Paul, Blackburn, Lancashire, England
Margaret Varah - [Child] of William Varah & Rebecca
    Born: 12 Jan 1849
    Abode: Blackburn
    Occupation: Earthen Ware Dealer
    Baptised by: Thomas Sutcliffe Curate    
Margaret Veary possibly married John Lowther - it is not like they are blood relatives, only marriage relatives and it would be in keeping with a gypsy tradition. This is how Margaret Lowther (nee Veary) could be a daughter on the 1871 census
----> IGI familysearch
Margaret Varey
England Marriages, 1538–1973
marriage:   20 October 1866   Parish Church Of Ulverston, Lancashire, England   
father:   William Varey
spouse:   John Lowther
other:   Charles Lowther
*Charles Lowther is John Lowthers father.
IGI
John Lowther
birth:   20 January 1848   
christening:   27 January 1848   Ulverston, Lancashire, England
residence:   1848   Ulverston, Lancashire, England   
father:   Charles Lowther
mother:   Ann Lowther
and his little brother
Robert Lowther
birth:   26 Mar (1859 ?)   
christening:   17 April 1859   Ulverston, Lancashire, England
residence:      Ulverston, Lancashire, England   
father:   Charles Lowther
mother:   Ann Lowther
So the 1871 census makes sense to me Rosie 

Also Mary, Ann, Jane ? in 1851 could all be with Lowther relatives in the census somewhere else