The Schism of the Commonwealth refers to the splitting of the British Crown between the United Kingdom of Great Britain and Ireland on the one side, and the British Nations Beyond the Seas on the other side.
The Schism got its start with the Abdication Crisis of Edward VIII. Having been forced to abdicate, his brother, Prince Henry, became King Henry IX (*here*'s George VI had already become King Albert of Russia).
While King Henry IX was a good king, he was seen as too weak by many in Britain, particularly after the rise of the militaristic Imperial Party, which dreamed of the restoration of British power. The abdicated King Edward VIII took a liking to this party, and joined it early on. Upon taking control of Parliament, the Party rammed through the Edward VIII Restoration Act, officially restoring Edward VIII as King of the United Kingdom of Great Britain and Ireland. The other Commonwealth Nations refused to recognize Edward VIII as king, and their parliaments passed acts supporting Henry IX, who left Britain to settle in Canada (later left for Sydney, Australia when it became clear that the United States would be an enemy in the upcoming war). Neither side ever recognized the validity of the other, and threats of civil war festered, until the start of the Global War, when the two sides set aside their differences. On December 2, 1946, when Britain overthrew the monarchy, becoming a Republic, thereby ending the Schism. Proposals to restore the monarchy in Britain have been made on several occasions, but rejected. Today, the King of the British Nations is Henry's eldest son, King Wiliam V.