The government only works because of the faith, and trust people have in it. Well, they have destroyed that,

In OUR eyes they have destroyed that. Step 1 is getting an ACTUAL majority of the people to lose faith in government. The shortcut is convincing the Canadian military or a shit ton of mercenaries that the government needs to be overthrown.

Also, as E_JACK stated, other governments need to recognize your government, because they'll continue to deal with Trudeau otherwise.