Canadian prohibition law allowed canadian companies to produce alcohol for export which notably involved smuggling to the US. To the extent that a handful of canadian alcohol producers are still associated with it, Sleemans and Canadian Club in particular.
Did the American government try to stop alcohol production in Canada? Was there diplomatic pressure to change that portion of the law?
There's actually a really good new book that you might consider looking up if you get a chance. It's called Bootleggers and Borders: The Paradox of Prohibition on a Canada-U.S. Borderland and was written by a guy named Stephen Moore at Central Washington University. It's a beautifully illustrated and slick publication from the University of Nebraska Press (one of the better academic presses in my view, but that's because they publish so much Alaska/Western stuff).
In any event, Moore argues that the "paradox" was the way that conflict over prohibition rules between British Columbia and the American states in the Pacific Northwest ended up creating closer relationships among them. At the start of American Prohibition, British Columbia (and other Canadian provinces, for that matter) had their own prohibition laws. British Columbia ended its prohibition laws in 1921 because ─ as Moore suggests ─ the demographics of the province tended toward single, working-class men, Anglicans and Catholics who were not all that opposed to the sale of alcohol.
After 1921, there began to be immense amounts of smuggling across the border, particularly the maritime border, which was impossible to patrol adequately. In 1923, there was a massive Canadian customs scandal related to smuggling that almost toppled the Canadian government. A significant number of hearings were held in Vancouver to investigate the matter, and these get some pretty decent treatment by Moore.
In any event, between 1923 and 1933 there's an immense amount of smuggling and smuggling-related violence, most notably the incident of the Beryl G, a smuggling boat whose Canadian crew was hijacked and murdered by Americans. There was a dawning awareness on both sides of the border that cooperation was the best way to deal with this violence, even as smuggling continued, hence the paradox. On one side, the Americans and Canadians were opposed on the issue of Prohibition. On the other, they had a vested interest in working together to quell the violence.
Moore's definitely worth picking up if you're interested in something that looks "away from the center" in Ottawa and Washington, D.C.