Hi Lisa,
Ironmongers did have a Guild which did have a Crest and possibly more local Crests. Hope this link works, if it doesn't, just Google The Worshipful Company of Ironmongers and check out the Archives and the Wikipedia articles.
https://www.ironmongers.org/archives

I seem to recall seeing somewhere..?? a Samuel linked with the store but he was born in the early 1900's (after the Samuel B:1870) maybe he is the connection you need.
HAPPY HUNTING:sleuth_or_spy:

Regarding the badge, we’re the family Methodists? Could it have been the badge of some Temperance Association or something?

Heths

Yes..I believe they may have been Methodist..that might be a possibility.
Thank you

From a Sheffield Newspaper dated January 19, 1876.
Marriages: Coates-Beedham, December 25, at the Baptist Chapel, Glossop Road,
by the Rev. J. M. Stephens, B.A. William Joseph, eldest son of William Coates,
to Lydia, eldest daughter of Jabez Beedham, Sheffield.

Moira.