Kingdom of Canada
The Kingdom of Canada was established in 1867 upon the consent of Queen Victoria of Great Britain. The status of Kingdom was originally meant to bring Canada as a personal union with Great Britain, granting it the same status as Scotland and Ireland. However, many in the British parliament objected to this status. Queen Victoria's personal opinion was that Canada would be better placed under a British prince as king. As such, her second son, Alfred, was selected to be king of an independent Canada.
Culture
The Royal Cnadian Mounted Police are a well-known symbol of Canada, being formed in 1873. However, the usage of the Mounted Police had been controversial, as they were used to subjugate the native population. Under Prime Minister John A. Macdonald and Minister Superintendent-General of Indian Affairs Hector-Louis Langevin, the Canadian government placed significant measures to pacify and aglicise the indigenous populations. Children were forced from there homes to church ran schools, where they would be scrubbed raw, made to wear European clothing, and forced to speak English. It is unknown to what extent the crown was aware of the incidences, but the monarch held little power in the ways of indigenous affairs.
History
The North American colonies had increasingly been seen as troublesome for British governance since the American War for Independence. The proclamation of Oregon to be a separate republic, claiming much of claimed but sparsely settled British Columbia and the Northwest Territories in the process, increased irritation among the British government.
In 1815, at the outbreak of the War of the North, the British government began to increase suppression of Canadian independent rule. The Governor General of Canada was established during the joining of the Provinces of Upper and Lower Canada in 1841, following a brief series of Canadian revolts against the established governments.
Beginning in 1864, many Canadian officials began to petition the British government for home rule. The idea was to establish Canada as its own dominion within the British Empire. However, the British Parliament felt the territory was more trouble than it was worth, and wished to invest in the more profitable territories in India. Queen Victoria offered to elevate Canada to the status of a Kingdom in 1867, and Prince Alfred, Duke of Edinburgh, was selected as king. Alfred was told of the announcement while on a Royal Tour for his mother, and did not arrive in Canada until 1870. In his stead, the posts of Prime Minister and Governor General were conjoined.
In 1874, King Alfred married Grand Duchess Maria Alexandrovna, causing much outrage in Canada and Britain. Alfred's mother was against the match on the grounds of Maria's Orthodox faith as well as Maria's position. Alexander Romanov, Maria's father, was also against the match on the grounds of anti-British sentiment. The Canadian Parliament was against the match since Maria and her family were at the time in exile for patricide and regicide. The couple had only met because Alexander was in the German States attempting to garner support for a potential uprising against Russian. The two were wed, however, and Maria joined Alfred in Ottawa. Upon the declaration of the Ukrainian Tsardom in 1883, Alfred recognized the state and extended diplomatic relations to his brother-in-law.
In 1899, the king's only son, also named Alfred, killed himself by gunshot. The king's eldest daughter, Marie, was made to renounce her claim to the Canadian throne as she was married to the King of Romania, Ferdinand I. The next eldest daughters, Victoria and Alexandra, were married to a German Grand Duke and Prince respectively, and so having them ascend to the throne would technically place Canada subservient to the German Empire. However, Victoria's divorce allowed her to retain her claim.
In 1915, on the onset of the The Great War, Victoria was urged by her mother, the dowager queen, to support her cousin, Nicholas I of Ukraine, and the Canadian government still felt a sense of kinship with the British. However, with the defeat of the British in 1920, the Canadian government and monarchy lost much of the goodwill of the citizenry.
Following the Great War, and the rise of Vladimir Lenin in France, Holland, and Occitania, Canada became reactionary and attempted to suppress the French culture in Quebec.
The national sentiment of Canada had grown to the point of attacking anything that wasn't seen as Anglican enough. Queen Victoria had initially named her son Vladimir after his Russian roots, but after outcry from the citizenry and parliament, the name was changed to Walter. Victoria was also hesitant to give Royal Ascent to the anti-Quebec bills being passed, but was eventually convinced by parliament that the protests and riots, such as Montreal Riots, of the Quebecois was evident of their violent nature.
Beginning in 1933, Britain, officially the Anglo-Irish Empire, demanded aid from Canada to suppress Irish nationalism in the Irish War for Independence. Queen Victoria refused, citing a more isolationist and nationalistic policies. Therefore, Ireland gained its independence in 1936. It was among Victoria's last acts as queen before passing away, leading to the ascension of Walter.
When Great Britain formed the Commonwealth of Nations in 1941, Walter and the Canadian Parliament debated joining. Ultimately, it was decided joining the alliance had more benefits than isolation in the Americas. This came as a challenge following the Battle of Guam and Great Britain's declaration of war on America. Canadian politicians understood that joining the war placed Canada on top of the list for invasion. It was therefore decided to terminate their place within the Commonwealth alliance and declare their own neutrality. This sentiment went as far as changing the national flag to exclude the Union Jack.
Foreign Relations
Upon the establishment of the kingdom, King Edward I of America attempted to have King Alfred sign the Continental Ordinance. However, Alfred refused, believing it would alienate Canada from British assistance, and place Canada under the dominion of American foreign policy. Thus, he believed it was best for Canadian sovereignty to decline the Ordinance.
In 1870, Alfred signed a treaty with Oregon, ceding claims to British Columbia and the Yukon Territory, as he believed the area would be difficult to defend from the republic for little gain. Canada's access to the Pacific Ocean was thereby lost.
In 1893, The Kingdom of Canada was one of the largest protesters to the overthrow of the Kingdom of Hawaii. Canada refused to recognise the newly established republic, though could not move to reinstate the monarchy for fears of rising tensions with America. When the monarchy was restored in 1909, Canada pressed to have Hawaii not be forced to sign the Continental Ordinance, keeping with the belief the document would put the islands under American control indirectly. As such, Hawaii refused to sign the document, and sought protection from the Empire of Japan.
Following the Great War, Canada's relationship with Gran Colombia soured as the latter became a haven for fleeing Quebecois from reactionary oppression. Canada faced geopolitical isolation in the New World for the measures, particularly from Haiti, who had retained much of their French Creole culture.

While I object to my province not being included in the Kingdom of Canada on principle, from an alternate history reasoning standpoint, I cannot fault your logic. Well considered, well done!