Hi Trees,
I dont have access to Parish Records and hopefully someone else does

All info Familysearch Pilot;
CAROLINE Hollyoak, Christened/Baptised 10 June 1827, Kings-Norton, Worcs
Parents ABRAHAM and SUSANNAH
IGI has the Christening 10 June 1827, St Mary, Moseley by Birmingham, Worcs
Now they may have Married Warwickshire;
Abraham HOLYOAKE
Susannah PARKES, 27 August 1818, Aston Juxta, Birmingham, Warwickshire
I cant find Thomas/Williams Christenings with my resources but in 1851 Thomas born c 1823 Kings Norton is with Mother Susannah.
I will post as transcribed;
1851 Census
?wick St Bordesley
Aston, Warwickshire
HO107/2060/313/35
Susanet HOLYOAKE, 62, Head, Widow, born Kings Norton, Worcs
THOS Holyoake, 28, Son, Unm, Ag Lab, born Kings Norton, Worcs
1851 Census as you said WILLIAM Holyoake born c 1821 is with Wife Eliza and Family;
HO107/2024/588/36
1841 Census
Kings Norton, Worcs
HO107/1197/21/Kings Norton
Abraham HOLYOAKE, 50
Susannah, 40
Thomas, 20
Caroline, 14
There is something strange on some Family Trees

Back soon.