For a continent-spanning Empire, how about aborting the Louisiana Purchase? SAy the US a and France for some reason get into another spat and the deal is off. France was nmopt on the best of terms with the US anyway, and Haiti was a particular worry for the Southern slave states IIRC, even back then.
There may or may not be a war of 1812. Let's assume there is, and it ends in a draw as OTL. After defeating Napoleon, the British get Louisiana as spoils of victory. This creates some serious tension with the US. There is a revanchist war in the late teens on the mistaken assumption that 'we almost whipped the Limeys last time', which ends rather badly for the US despite considerable initial gains in territory. Tension keeps simmering, and of course there are still settlers building up the US, to the point where Britain is very, very nervous about the viability of her American possessions (the West never gets developed to the same degree because the Mississippi is not as open, being a border for much of its length). The US, on the other hand, are putting together an alliance securing Russian goodwill and Mexican support for their 'Rockies or Bust' move. This time they almost make it, but only almost as British diplomacy and bribery overthrow the Meaxican government and pull out the rug from under Uncle Sam's feet. Peace is sought and granted on lenient terms, mostly at the instigation of the Northeastern states suffering heavily from blockade and naval forays. Britain gets to keep Louisiana, integrated with Canada, and receives Alta California with its excellent deep-water ports in addition to Oregon. The Mississippi is neutralised and demilitarised. The US get to take their revenge on Mexico at leisure - their strategy is now oriented south, no longer northwest.
We all know what is liable to happen in California sometime soon, so the economic development of this new continental power gets a nice fillip. Take the US out of the picture with internal troubles (quite likely in a country that, instead of the unbroken chain of successes of OTL, has suffered humiliating failure) and allow the British to extract Alaska from the Russians in the Crimean War (always assuming these things still happen).
The latter half of the nieteenth century is going to be an interesting time, with Britain working hard to build up population in Canada while the US are considering whether they can risk a grab, but eventually the two sides are liable to recognise they have more to gain by trusting each other. After all, the US is about business, and they need Canadian Pacific ports for their shipping, ties into the Canadian railway networks, Canadian lumber and metals, and free navigation on the Mississippi. The Canadians need relief from disproportionate defense burdens and a quiet sleep despite the population and industrial giant to their south and east.
Copme the twentieth century, Canada receives Dominion status and independence. The motherland's parting gift are its Pacific territories, from the Sandwich Islands to Samoa, now administered from Ottawa. It has taken a century of conflict - and finally, world-spanning conflicts fought and won as allies - for the US and Canada to see eye to eye, and even today, there are many US Americans who worry about the industrial development of Canada's west coast. Steel mills in Oregon and Lakota and factories in California are competition for the established Eastern manufacturers, anmd many highly skilled young workers are already tempted to move there by sunny climes and high wages. Canada's dominance of the Pacific, on the other hand, is no longer a policy issue after the twentieth century has shown that the two nations work best in defense synergies - US ships defending the Atlantic sea lanes and controlling the Caribbean approaches to the Panama canal, Canadian ones controlling the Pacific and bringing war to the Eastern enemy.