I expect this is my last post on this topic...
Re an alliance with the Soviets, in a world where the U.S. the attacks a dominion of the UK with poison gas I suspect the UK would be looking for any allies they could find. If the Soviets can be pursuaded to side with the UK (perhaps in return for getting to keep Alaska at the successful conclusion of the conflict) then the UK gets a strong continental partner who could presumably help keep the Germans in check while the UK deals with the U.S. I suspect the geo political goals of the UK might change in the event of a war with the U.S.
I suspect the U.S. is going to be looking for allies as well. Perhaps they ally with Germany ?
Still, why would the Soviets be that desirous of Alaska that they'd go to war over it? This is about the same time they considered selling off Kamchatka and Chukotka to help with the rebuilding of the USSR. It was all nearly the same...
If you want to tempt the Soviets into war to fight and die to save the capitalistic pigs *fingerquote*, you need to offer them something far more substantial than Alaska, which has practically no value to the Soviets aside from being formerly under the control of the Russian Empire - that great state they tried to emulate. To that end, you'd have to promise a cessation of British support for the states of eastern Europe - offering up the Baltics and Poland to the communist menace. That's the kind of deal that would get the Soviets on board for a token show of force.
As it is, you're dangling peanuts for the Soviets and hoping they invest significant time and treasury for a reward that isn't worth it. If the British were that desperate to ask, the Soviets would tell them to increase the offer, not take it.