RootsChat.Com

For a divorce in England'Wales, you can try searching your names on https://discovery.nationalarchives.gov.uk/ but I woudn't personally hold my breath.

It's very likely there was no divorce. The hurdles for the average person (financial, legal, societal) at this time were just too high compared to the relatively simple and face-saving solution of just going somewhere that nobody knew about your first husband and saying you were widowed. There would have been no way the registrar could have cross-checked the information she gave, unless someone locally knew her history and was willing to dob her in.

Have you sighted the 1915 marriage certificate? How is she listed there? If she is "single" or "widowed", you can presume there almost certainly was no formal divorce.

It sounds like these folks would have been members of Lonodn livery companies (Worshipful Company of...)

Records of these are often very handy as they cover how they became members (e.g. through apprenticeship, or through their father).

For example, here are all the Coopers listed as apprentices in Worshipful Company of Carpenters records from 1654-1694.
https://www.british-history.ac.uk/no-series/london-carpenters/1654-94/pp201-224
Cooper, Edward, 21, *152, *190; Elizabeth, *81; Francis, 180; George, *105; Godhelpe, 161; James, *180; John, *5, *134, 152, *161, *198; Prudence, *78; Rebecca, 156; Richard, 23, 40, 59, 76, 83; Thomas, 20, 156; William, 9, 57, 69, 78, *79, 81, 86, 91, 127, 147, 190.

entries take the form of:
Edward Cooper the sonn of Edw: Cooper of Stratford upon Avon in the County of warwick malster hath putt himselfe appntice to Christofer Lockwood for seaven yeares from midsomer day instant.

His death certificate would likely be the only item guaranteed to list this info. Except where there was an accident, mostly papers would only say things like "suddenly" or "after a long illness" at most.

At paperspast.natlib.govt.nz a few notices exist, no particular mention of nature of death.
https://paperspast.natlib.govt.nz/newspapers/NZH19131216.2.2.3?items_per_page=100&query=%22Catherine+Gillespie%22&snippet=true&sort_by=byDA
 - confirms he died at the hospital.

Incidentally I can see his marriage in 1911, but no children.
https://paperspast.natlib.govt.nz/newspapers/NZH19420331.2.2.3?items_per_page=100&query=%22Erna+Veronica%22&snippet=true&sort_by=byDA
 - this Erna Kennedy nee Gillespie, whose mother was Catherine, is recorded in NSW deaths as the daughter of a George.

https://archives.aisne.fr/archive/resultats/RMI/n:151?RECH_nom=Sonet&type=RMI
son Charles in 1910 (mother listed as deceased, father "Auguste" Sonet not listed as deceased) and Pierre in 1912.  At this time they were both resident Villeneuve St. Germain - if you look on the bottom right there is a list of successive addresses for them.