One critical point no one seems to mention is it depends how quickly the US mobilised. For instance, Canada could field a larger home army than the US, and a lot of these are situated right next to American populace. In fact, the Canadians should have an early advantage, the more territory they take the better the odds and the less men America can mobilise. Especially on the East Coast where Canadian troops are more focused. Nonetheless it's a big distraction for troops, but in the running Britain certainly will not leave it's Canadian ally by itself. America most likely would have decided that Canada would be easy to beat just like in 1812 and not bother to mobilise much, before it is beaten back and then begin to mobilise. It would be focusing on it's navy to this point, as the British Navy is more a threat than the Army.
But here we have a Canadian army storming through the east coast, the US army was even smaller than the Portuguese in 1940, and in 1941 it still wasn't that great. It would take a little while but Canada would probably get halfway down the east coast before it is stopped denying a crucial amount of manpower from the US and getting some potential support from those who are anti fascist. Now it would likely become a stalemate, but this distraction would likely cause a lost African front, with Britain managing to hold onto one side of the Suez and that's it… so once again we arrive at a huge what if. British supplies now get diverted the long way round. It's a matter of time. Will the US capitulate first or will Britain run out of supplies first? By 1942 the two forces would be in complete standstill and by 1943 British tanks and aircraft should be slightly overpowering that of the US, well, that which the Brits can manage to supply anyway. Fact is a direct engagement between Britain and the US would be incredibly devastating to both sides navies, but I feel Britain with experience already against Germany, Italy and Japan would likely get the early advantage, but again, if the USA continues to pump out ships the UK is in trouble. But then again Britain can also hit Panama from Belize.
In this instance, I feel China would eventually reach stalemate with Indian support coming through, and Russia would eventually win but if Britain and Russia were to win, it would take until 1948 minimum, with Russia taking all of Europe apart from France and Greece, and Britain splitting the United states up or even taking parts of it. If the Allies still won it would be a very economically distraught world where anyone could have become a superpower. Most likely Britain and Russia still but they would not exert any influence for decades. In fact the cold war would likely begin in 1960.