I can`t find a suitable Joseph Sixsmith living in Lancashire born c.1828 in the 1841, 51 or 61 census.
Here's a Joseph & Emma born c 1821 on the 1841 census Surname transcribed as SEXSMITH
HO107; Piece: 521; Book: 5; Civil Parish: Warrington; County: Lancashire; Enumeration District: 3; Folio: 8; Page: 10
G? House Row Warrington
Alice SIXSMITH 50 Washerwoman
Thomas " 17 Ap.
Joseph " 20 can't make out his occupation possibly glass maker
Emma " 20
Joseph Sixsmith Christening Date: 27 Aug 1820 St Elphin Warrington Lancashire
Father
Daniel Sixsmith Mother
Alice Abode: Bank Quay Occupation: Glass Maker
Thomas Sixsmith ch date 1 Feb 1824 St Elphin, Warrington, Lancashire, England
father Daniel Sixsmith & Alice
Abode: Bank Quay Occupation: Glass Maker
and possibly Emma in 1851
1851 HO107; Piece: 2231; Folio: 312; Page: 2
Emma Sixsmith married 30 Manchester
Thomas son 6 Manchester
Alice dau 3 Manchester
James Stanley son 14
Edward ditto 9
1 servant