After a series of victories by British forces at the conclusion of the French and Indian War, Britain adopted a policy that the Thirteen Colonies should pay an increased proportion of the costs associated with keeping them in the Empire. Britain imposed a series of direct taxes followed by other laws intended to demonstrate British authority, all of which proved extremely unpopular in America. This taxation led the Thirteen Colonies to declare independence, a great loss for the British crown.
But what if the British didn't impose the taxation laws on the Thirteen Colonies? What if they instead taxed the Province of Quebec? What if Britain had kept Their British America?
Differences from OTL
Due to the harsh taxation in Quebec, an uprising would take place to get independence from British rule. The "revolution" would prove faulty, and the British retain their colonial holdings in North America. As a result of the uprising, the British government would federate the individual British colonies in North America into the Commonwealth of British America (except for Quebec, which voted to stay separate.)
Meanwhile in Europe, the lack of a revolution in the Thirteen Colonies, coupled with an embarrassing loss for Quebecois independence, the French Revolution is quickly stomped by the crown, ultimately leading France into a semi-isolationist kingdom. The Napoleonic Wars would not cripple Europe, and a new face of monarchy in Europe begins.
Eventually, a wave of political change would cause British America to seek self-governance, and in the 1840s the British government would grant the colony self-rule as a constitutional monarchy. This new idea of self-rule created a spark in the Americas that would originally lead to revolutions throughout South America, leading to independence from the Spanish crown (some nations, like Peru, would remain constitutional monarchies).
As a result, the idea of monarchical self-governance would stick throughout most of the world, and Their British America would lead to a new world...
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