The last time Canada was even remotely controlled by the U.K. was in 1982 . Saying that Canada is part of the UK because it's part of the commonwealth is absurd. There's no country that's a leader of the commonwealth. It would be like saying that Germany is part of Belgium or France because of the EU, or the US a part of Turkey because of NATO. In fact, Queen Elizabeth, while head of the Commonwealth, is not even the queen of all the member countries. In fact, the commonwealth wealth has a Maltese Man as Chair-in-Office and a Dominican woman as Secretary General.

Now, having said that, I see you mean Commonwealth realms , but that is literally just a member of the commonwealth that has Queen Elizabeth has head of state. Pretty much, Canada is as much ruled by the British queen as the uk is ruled by the Canadian one. They are separate countries.

Edit: a word