I think this is the same family in 1851 living at St James Place, Aston Near Birmingham and I noticed son Joseph had the same birthplace at Mary A Underwood in 1861
Sarah Reader Head Married 35 Pershore, Worcestershire
Sarah Ann Reader Daughter 12 Birmingham, Warwickshire
Alice Reader Daughter 6 Stony Stratford, Buckinghamshire
Joseph Reader Son 9 Brierley Hill, Worcestershire
Ellen Jane Reader Daughter 0 Birmingham, Warwickshire, England
In 1851 I also found a Mary Reader age 13 b Birmingham working as a servant in Aston and poss sister Elizabeth age 15 was also working in Aston as a servant
Son Joseph James Reader was born 6 Jan 1843 and baptised 20 Feb 1853 at St James the Less, Ashtead, Warwickshire(part of Birmingham) at the same time as sister Sarah Ann. The parents were listed as William and Sarah address St James Place. William is listed as a boatman - preumably why he wasn't at home in any census - although poss in hospital in Birmingham in 1851 age 43 a boatman b Birningham
Kay
Added - I can find birth registration for Sarah Ann and Joseph James (as below) with mother's maiden name Badger but their sister Mary may have been born pre registration
READER, JOSEPH JAMES mmn BADGER
GRO Ref: 1843 M Qrtr STOURBRIDGE UNION Volume 18 Page 464
Poss death of William Reader
Age 54
Address Duddeston
Burial Date 16 Aug 1863 Saltley, St Saviour, Warwickshire
On the Underwood/Ready 1857 marriage cert no details were listed for bride or groom's fathers and this appears on quite a number of the marriage certs in the same parish so it may have been an error