The key to the USA peacefully annexing Canada is a German victory in the Battle of the Marne in 1914.
Don't know WWI Western Front in 1914 well enough, but here goes. The German offensive goes off as in OTL, but in TTL it's like 1940 26 years early. The Belgians fall apart very quickly. The British and French arrive in pieces and are defeated in detail in Flanders. The French are actually more successful with Plan XVI than in OTL, which just means they get a bit father away from the action by driving deeper into Alsace and Lorraine. The Germans sweep down, and, as in OTL, the French create their 6th Army to defend Paris. The Germans are in better shape than in OTL, and the Allies have less on their right flank, so the Germans win the Marne.
All is not well, however. This is not 1940. The French retreat into Paris, screaming defiance at the Bosche. The BEF and some other French forces reform along the Seine, and the French pull back from Alsace. The Western Front stablizes - at one point the line actually runs through the Paris city limits - into the trench warfare we all know and love.
Rather more of France - and the French population - is occupied by the Germans, and Paris becomes TTL's Verdun, Ypres and Passchendale all rolled into one. The Germans HAVE to have it. The French MUST keep it. Military logic (never a strong suit for either side in WWI to begin with) is completely abandoned in the name of PARIS!
With more of France occupied, the British (and Commonwealth) are forced to field larger ground forces in France. This butterflies away Gallapoli (the British are content to contain the Ottomans in the Med), but does nothing to curb Churchill's ambitions or the legimate strategic need to get aid to Russia.
Churchill concieves a bold plan. Seize Schleswig-Holstein! The idea being that several benefits would occur:
1. The Jutland peninisula can be held with relatively small numbers of troops - Trench warefare has proven the power of the defense.
2. It will open Baltic to Allied shipping - aid to Russia.
3. It will draw the High Seas Fleet out into the open where the Grand Fleet can engage - and destroy - it.
4. It will serve as an Allied beachead on Imperial German soil, giving a propaganda front to counteract Paris.
The Imperial War Council of Britain laughs this plan off, until 1917. By 1917 it is clear things are Not Going Well. Jutland and the Zimmermann Telegraph have been butterflied away. The Kaiser is unwilling to risk his pretty ships when things are going well on land. Italy is neutral, the Austrians are suffering, but holding against the Russians. Russia is visibly wilting, and in their mania to hold Paris, the French are giving ground in other sectors. The only strategic asset left is the RN, and it's time to use it!
With America firmly neutral, the British decide on a toss of the dice. In July 1917, the RN sorties into the North Sea. It is a disaster. The Germans got wind of the plan, and were waiting with Uboats, minefields, the High Seas Fleet and even bomb-carrying Zepplins. The British Fleet is trashed; the troops never make it ashore, and the whole thing is called off.
The disasterous operation coincides with the fall of Paris to German infiltration tactics, and Russia's descent into Civil War. On November 11th, 1917, the guns fall silent, and The Allies are forced to the negotiating table.
The Germans are harsh. They annex Belgium, get the Congo, and some reparations. They also get some choice bits of the British and French Empires. Malta, Madagascar, the Falklands, Jamaica, and Halifax and Nova Scotia, to name a few.
At this point, things get strange. As the terms are published, the United States suddenly stops navel-gazing and perks up. The German ambassador in Washington DC is informed that any transfer of soverienty in the New World would violate the Monroe Doctrine. The Germans, a whole lot less interested in what the US thinks now that the war is over, politely inform the US to Sod Off. Oh, sorry, that vocabulary is for Brits. Piss Off is perhaps more appropriate for Americans. When this is reported in the Hearst papers, it's like the Red Scare 40 years early. Wilson is under pressure - Action Must Be Taken to Prevent the Surrender of North America to the Barbaric Mustached Germans!
The Canadians are aghast at this, but they lack the power to say anything. The Germans load some troops up, and set sail for the New World. Wilson - AMBTPSNABMG - firmly in mind, decides that no, this will not happen.
And then the USN sorties. Though no where near the size of the prewar RN or SHF, the alt-Jutland devastated both fleets, and the USN is now bigger than the HSF. The Kasier, flush with victory is not prepared to have His Navy back down to a country that, in the words of one soon-to-be-infamous German NCO, didn't have a big enough army for a good German parade.
Things look headed for a showdown when cooler heads prevail. Willy II is not informed when the Germans approach the British with a way out. No one (besides Willy II) in Germany wanted another war. Britain is strapped for cash, and the Germans don't want a war with the US. The Germans, therefore would not consider a breach of the terms of the treaty is Britain sold Canada to the United States, including Halifax and Nova Scotia.
The Canadians are aghast at this, and it isn't really legal given the Dominion Act of 1867, but becoming a part of the USA is preferrable to German occupation.
So, for the price of $1 Billion (quite the sum in 1917), the USA buys Canada. The USN and HSF do not confront each other, and the USA doubles in size. Willy II is thrown into a rage by this, but he still contents himself with Jamaica and his other spoils, so gets over it.
How's this?
Mike