The Monarchy is "shared" amongst Commonwealth countries. It does not confer any control over Canadian affairs whatsoever to the UK government. Although Canada became a "country" in 1867 with the British North America Act (BNA Act), many aspects of Canadian governance were retained by the British government, such as foreign affairs. That's why when the UK declared war on Germany in 1914, Canada was automatically included.
For all intents and purposes, full independence came with the Statute of Westminster in 1931. When WW2 broke out, Canada made her own declaration of war. The BNA Act remained our constitution until 1982, because that's how long it took for the provinces to agree upon an amending formula. Until that year, when the Canada Act became law, a few vestiges of British rule remained. For instance, at the request of the Canadian Government, an amendment to the preceding constitution (BNA Act), had to be passed by the British parliament, since it was a British Act.
As for being the "most operationally sound democracy in the western hemisphere"...maybe. But, extremism is contagious. So, please get your poop in a group (as a country, not you personally) before it takes root up here.
Thank-you.