Similarly, Poland once occupied Moscow in the distant past and has managed to persist as a distinct nation, though the Russian calculus sometimes worked out against Poland such as during Russian-Prussian or Soviet-Nazi alliances.
Ukraine and Russia have their own history yet Ukrainians have managed to valiantly persevere as we can witness today. Unfortunately for geographic reasons the strategic calculus there is much tighter than US-Canada or Russia-Poland.
By the British, not by "Canada" (which didn't exist).
To put another way, even had the US not invaded British North America, the UK would still have attacked Washington as part of the overall war. The one did not cause the other.
The strategic reasons for a potential attack are similar, and the same risks remain.
The US invaded and failed. Had they succeeded I doubt the British would invade Washington vs strengthening their position in the remaining colonies.
The modern and even pre-modern history of Ukraine is inseparable from a degree of violence that only existed in north america when directed towards slaves and indigenous population. There are not centuries of built-up ethnic/nationalistic turmoil between the U.S. and Canada, although I'm sure you could find some crazies who've convinced themselves there must be.