Actually, the Queen was historically rather more involved than this in the era of Hume, Macmillan and Eden; and previous monarchs before her even more so.

I agree that in the current era though, she would only send for an alternate PM if they had demonstrated confidence of the House of Commons, which is very unlikely.

That's the major difference between Presidential systems and Parliamentary ones. In the first, the head of government is directly elected and the legislature separately, and in the latter the legislature chooses one of its own as head of government. Semi-Presidential systems (like France) are somewhere in between.