There's also the problem the US and UK face of Canada deciding, as they did in our timeline, that they are not obliged to take part in a war just because Britain asks them too.
If the US activates War Plan Red because they decide they want new states in the north, then yes, Canada will fight. If the war sparks over some crisis caused by balance of payment disputes or Venezuela or what have you, Ottawa may well wash its hands of the affair.
That will leave the US with the choice of either invading a neutral democracy, which won't be popular at home or internationally, or having to fight the war entirely in the Atlantic and Pacific- which they will eventually win, but not without a great deal of pain.
The UK may well prefer that Canada stays out, actually.