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https://archive.org/details/bluebook191000dauuoft/page/n157/mode/2up
In 1910, 332 Bay Street South was the home of Mr and Mrs F. W. Gates (Junior)
Miss Gladys and Miss Dorothy Gates, as well as Alexander Frederick Gates.

in 1901 you can see Gladys with them
http://central.bac-lac.gc.ca/.redirect?app=census&id=35673902&lang=eng&

She was Gladys Mary so could have been G.M.
https://www.familysearch.org/ark:/61903/1:1:XLTK-98N?lang=en

Now, the other three children married in Ontario, but Gladys was unmarried in 1921 at the time of her mother's death (she seems to have used the welsh spelling Gwladys later in life)
https://www.familysearch.org/ark:/61903/3:1:3Q9M-C3MW-D32Q-Z?lang=en&i=2371

And here is proof that Gladys was in the country - she left Canada May 24th 1921 for "holiday" and returned home 12 August 1921.  Perhaps the families knew each other in Canada.
https://central.bac-lac.gc.ca/.item/?op=img&app=microform&id=30927_2000901365-04116

( https://www.bac-lac.gc.ca/eng/discover/mass-digitized-archives/ocean-arrivals/Pages/item.aspx?EntryName=Gardiner%2c+Rachel+-+Gaunt%2c+Lydia&PageId=3445762 to go through all the items, it looks like she made a couple of journeys in these years and her father did as well and I think was with them in 1921)

There would not be any records of trips within the UK.  But yes, it was very common for emigrants to have to cross (by sea, land, or both) to one of the big ports, rather than there being multiple stops on the way.

A bit of context for you about Plymouth as an emigrant port at this time:
https://devonassoc.org.uk/wp-content/uploads/2023/07/Brayshay-Government-Assisted-Emigration-TDA-1980.pdf

https://earlgreysfamineorphans.wordpress.com/tag/jaki-mccarrick/
 - A description of the conditions aboard the "steamers".

https://provincialarchives.alberta.ca/how-to/find-birth-marriage-and-death-records/marriage-indexes

Up to 1949. Handwritten indexes but if you know the rough year of marriage should be able to find them.

Regarding the "pink card", the only reference I can find is from 1908 and indicates that this may related to luggage and customs checks (see page 26).

https://recherche-collection-search.bac-lac.gc.ca/eng/Home/Record?app=cangaz&IdNumber=8597&q=%22pink%20card%22&ecopy=cgc_p1-2_v041_n000_t001_000_19080627_p00026