Canada was the next thing to independent in 1867. Yes it kept ties to Britain, extremely close ties in fact, but Britain couldn't just tell Canada exactly what to do, much less sell land.Ummm.... No. Canada doesn't become independent until ... hmmm... say, the Statute of Westminster in 1931 (one can argue the exact date)*, but during WWI, the UK probably has the RIGHT to sell Canada. Of course, it wouldn't work, Canada would likely declare independence. Still, the attempt would likely, ultimately, lead to a US take-over.
OTL, by the end of WWI, Canada was establishing its own identity (Canadian units officered by Canadians, instead of British, for instance), but I don't think Canada as 'its own country' was quite the dominant meme yet, although it was growing fast.
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*Granddad, who never took out Canadian citizenship for some reason, could vote in every Canadian federal election in his lifetime as a British subject. And, of course, there are those who claim that the repatriation of the Constitution was the formal dividing line.
After 1867 Canada had control of all internal affairs as long as they did not badly affect Britain. Selling off Canada is definitely an internal matter.
The part where it gets tricky is international affairs. Canada agreed to follow Britain in regards to international matters that did not affect it. If Canada was affected it would act as the junior partner to Britain.
This was shown in the Alaskan Border Dispute in the early 1900's. Canada had one diplomat and Britain had 2 in the border discussions with the US. Britain sided with the United States because Canada's argument was frankly full of hot air. But Canada did have a say in the matter, and if Canada had decided to ignore it they could have. But in that case Britain would have walked away and said "Its your problem now" and the US could do whatever it wanted.
If Britain had openly sold Canada or even parts of Canada, the Canadian people would have thrown the British out. Canada was fine being a junior partner on the world stage because being the junior partner to Britain still gave them a lot more power than being a tiny totally independent country. But this doesn't mean they were owned by Britain.
And I think the best way for Canada to join the US after the ARW is no War of 1812. Keep the American settlers coming in, keep the Family Compact out of power, and most importantly keep the immense amount of trade open between Canada and the US without fear of invasion and most of Canada is going to feel very cozy with the US. This doesn't mean they'll jump into the US with open arms, but a gradual economic union throughout the 1800's followed by political union in the early 1900's is possible.
Quebec would likely be an independent minded dominion of Britain and the Maritimes would stay British, but Ontario and the west would likely join the US, simply because of the economic benefits.