How they react to it would be the same way they react to any opposing-faction country; war and/or buildup of forces during a tenable peace.
As for what did they do to stop the situation, here's the deal: Canada joining the axis pretty much means Germany went whole-hog on their spy ring targeting Canada as their "choice of convert". The allies could have done something along the lines of "spies that support ruling party", but they currently (at least, not noticeably, I can't see behind the scenes) do not seem to. If only 1 country off-joins per game, however, then that's hardly the largest, or even currently deserving of programming resources, issue that should be worked on within the game.
Historically speaking, the UK certainly wasn't interested in making enemies of the USA. However, that doesn't mean the USA can't think of UK, or anyone else that UK brings into the allies (if, say, UK managed to convince Japan in or something) as enemies.
If UK brought Japan to the Allies (as a strategy to assist their ally Australia from getting attacked by them), and then Japan bombed Pearl Harbor anyway, I'm pretty sure the USA would go after Japan and UK. (Once USA found out what Germany was doing "behind the scenes"... like, things I can't discuss on these forums... they may have then decided to stomp Germany as well, but not till after the conspirators that actually bombed their property were taken care of).
Or, here's another one: Hitler had at least 1 major (though I'm sure there were many more behind the scenes) assassination attempt at him. If any of these had succeeded, and the still-facist-but-under-new-leadership Germany decided that, rather than blaming who they did for world events, they went whole-hog after Communism instead, and their war went straight to the USSR rather than the "friendlier" countries first... USA (given how the populace of then viewed communism) may have actually backed them "indirectly" in the fight (lend-leasing assets to Germany to fight USSR rather than to UK to fight Germany). The leadership of the USSR at this time wasn't known for level-headedness, and as Pearl Harbor showed, one big attack was all it took.
These are abstractions, of course (as there is no assassinate leader in HOI3), but still situations that may have happened. 1 briefcase 3 more feet to the right, and who knows.
That's why we have games like these