Simple answer - it's complicated!
The world was very different in 1776 than it was in 1867 or 1900.
The US war of independance followed the movement/ideas that led to the French revolution and was a real political/philosophical difference in how you should run a country. It was also concentrated in a few large cities with a large established political class. At the same time Canada, NZ and Australia were much more sparsely populated by people who were mostly much newer immigrants and still thought of themselves as British so there was no real 'independence' movement.
The formation of these three into separate countries was a much more gentle gradual process and generally fairly peaceful. I think there was a genuine feeling that their economies, population etc was big enough to stand on their own and there was no legitimate reason to stop them - better as friendly 'cousins' than prisoners.
India, the remaining bits of Africa and the Caribbean following WWII was more a combination of, "we can't afford them", "we just fought a war for freedom we can't really justify our own Reich" and the Bomb+Cold war makes the empire pretty irrelevant anyway.
Why Scotland, England, Northern Ireland and Wales didn't get separated then?
At the time? Because either their economies and population didn't support it or were much
much more interlinked with England's. Ireland is a bit of a special case - there were political/religious reasons for it being independent which overrode other concerns