Hello arborist -apologies for not Welcoming you on your first post
As Mo posted it is unusual for Mother's name to be on UK marriage cert - I would go as for as to say unlikely!!
I think I have found James -but mother's name "Louisa"

Maybe because harriet Chadwick was a witness on the marriage cert it was (mistakenly) thought she was james' mother _I believe she was his sister
1881 census shows James Chadwick age 26 stonemason b Rochdale with wife Sarah A and her brother Edmund Howarth -and other family -you can view this free on family search
also in 1881 there is
28 Church St Rochdale
Sarah A Douglas head M 32 River Cotton Rochdale lancs
Harriet Chadwick sister U 24 River Cotton Rochdale
RG11 4106 15 24
I believe these are james' sisters
1871
5 St John St Rochdale
John Stansfield head M 49 Iron Lab Todmorden lancs
Louisa Stansfield wife 52 Rochdale Lancs
JAMES CHADWICK son 17 stone mason Rochdale
Harriet Chadwick daughter 15 Cotton Operative Rochdale
RG10 4119 151 31
1861
6 nelson Square Rochdale
Louisa Chadwick Head W 50 Washerwoman Rochdale
Sarah A daughter 14 Back Tenter Cotton Rochdale
JAMES CHADWICK son 7 scholar Rochdale
Harriet daughter 5 Rochdale
RG9 3036 43 19
(next door are the Douglas family who Sarah A married into)
1851
Drake St Rochdale lancs
James Chadwick head M 40 Weaver & Greengrocer
Louisa wife 35
Sarah Ann daughter 3
Edward son 2
John son 9mth
all b Rochdale
HO107 2244 519 15
(Louisa's age varies from census to census but that often happens
Suz