Well DaV had a good idea in his timeline 'British Imperialism in the with Century"
Napoleonic Wars turned out rather differently with a stronger; though not dominating France and the UK was able to send Wellington to Canada to take command.
With a strategy with being friendly and appeasing the politicians and population New England when marching through and supporting Tecumsehs Confederation the War of 1812 ended with New England seceding and a Native State being established in Michigan(minus detroit) with bits of Illonis, Indiana and a good chunk of eastern Wisconsin. Though the Native state recieves a large population boost (and a centralized military)because of the US acting quicker and harsher to natives in US territory, which caused them to go join Tecumseh or settle in Canada.
So with that the US can't really touch Canada's population centres the UK is happy to support them both as buffer states.