Per the 1851 England Census, that year, the entire family was living at their tailor shop in 66 Jermyn Street. Since Sarah was born in Burton-on-Trent and her younger brother John Mousley was born in London, they must have moved when she was small. Both parents died in London in 1857, when she was still a child. 
In 1861, at 18, she and her younger brothers and sisters (John, 17, William, 15, and Catherine 12) were living in Burton on Trent, in Horninglow Street, with her aunt, Catherine Mousely.  Presumably they returned to live with family after their parents died. She and Aunt Catherine are still on Horninglow Street in 1871, but her sister Kate is not. 
Believed to have emigrated in 1873 with her brother Will and his wife Mary Elizabeth on the Cordova, along with her sister Kate and "Aunt Catherine" as a visitor. The three girls appear on the ship's records as three "spinsters," Miss C. Mausley age 55, Miss S. Mausley age 32, and Miss C.E. Mousley, age 25. 
Sarah Yates migrated from England to Louisiana.
According to family records she was a tutor and music teacher in the family of Captain George Locke at Lake Charles, Louisiana. "She was treated like a member of the family... Also her younger sister Kate and later my mother's older sister, May (Martha Ann) were invited to the great balls given in the Locke mansion."
CAN'T FIND - US Census 1880 Sister Kate is in Covington running the boarding house; John Mousley is on the farm with wife and kids; brother Wm. Henry is not on 1880 census. She is not on 1880 census in Lake Charles with George Lock family either.
↑ 1.01.1 Certified copy of Birth Certificate, Registration District: Burton on Trent, 7 June 2017
↑ 2.02.1 Ancestry.com. 1851 England Census [database on-line]. Provo, UT, USA: Ancestry.com Operations Inc, 2005. Original data: Census Returns of England and Wales, 1851. Kew, Surrey, England: The National Archives of the UK (TNA): Public Record Office (PRO), 1851.
↑ 4.04.1 "England and Wales Census, 1861," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:M7HK-7X8 : 6 April 2016), Sarah Yates in household of Catherine Mousley, Burton On Trent, Staffordshire, England; from "1861 England, Scotland and Wales census," database and images, findmypast (http://www.findmypast.com : n.d.); citing PRO RG 9, The National Archives, Kew, Surrey.
↑ 6.06.1 The National Archives at Washington, D.C.; Washington, D.C.; Passenger Lists of Vessels Arriving at New Orleans, Louisiana, 1820-1902; NAI Number: 2824927; Record Group Title: Records of the Immigration and Naturalization Service; Record Group Number: 85
↑ 7.07.1 Notes by family historian Juanita Gayer, given to Boone Yates Richardson, and uploaded here.
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It may be possible to confirm family relationships with Sarah by comparing test results with other carriers of her ancestors' mitochondrial DNA.
However, there are no known mtDNA test-takers in her direct maternal line.
It is likely that these autosomal DNA test-takers will share DNA with Sarah: