Today is Canada day, which to my understanding is when Canada celebrates their Independence from Britan (yes I am an American so sorry ahead of time if I am misunderstanding something)

This understanding is incorrect. Canada Day marks the Constitution Act of 1867, which created Canada as a federation by uniting the three provinces of British North America: Canada (subsequently split into Ontario and Quebec), New Brunswick and Nova Scotia. The Constitution Act gave Canada the status of a "Dominion," a semi-independent part of the British Empire which had some powers of local government but was still subservient to the British Parliament and the monarch. Most of the other "white" British colonies also received Dominion status - South Africa, Australia, New Zealand, and (until its union with Canada) Newfoundland.

The process of independence for the Dominions was a gradual one, as the local governments progressively asserted their independence from Westminster. The First World War was a significant turning point, and the sacrifices involved became totemic for the nationalists of each country - in Canada it was the Battle of Vimy Ridge, in Australia and New Zealand it was Gallipoli. The key thing to understand here though, is that this push towards independence wasn't particularly anti-British, given that dominant populations in each Dominion were either British settlers or descended from settlers, and up until WW1 tended to consider themselves as British as the people living on Great Britain. The aim was more for legislative independence from Parliament rather than a total severing of ties, and the British monarch remained extremely popular in the Dominions. This status was cemented by the Statute of Westminster in 1931, which finally ended Parliamentary control over the Dominions and created the Commonwealth of Nations. The Statute also established the position of the monarch as king/queen of all the former Dominions, and requires all of them to approve any change made to the laws of succession.

In other words, there was no revolt against British rule or push for "freedom" that would lead these countries to renounce the monarchy. Former colonies which have renounced the monarchy generally did experience strong anti-British movements - for example, in South Africa the Afrikaners are descendants of Dutch settlers conquered by the British in several bloody wars, and they were a driving force behind the country becoming a republic in 1961. In more recent decades, other Dominions have flirted with republicanism (Australia's 1999 referendum, where the country narrowly voted against becoming a republic, just makes it past the sub's 20-year rule) as the old ties with the monarchy become increasingly historical in nature.