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How to parse the phrase how come?
And can one use this phrase with auxiliary verbs as well as modal verbs?
That is to say, are these examples both correct?
How come are you sitting here when they're all vacationing?
How come can you sit idle when your friends are playing soccer outside?
The second sentence doesn't look fine to me.
This article explains some of the background to the set phrase how come. The article suggests that the set phrase might be an abbreviation of "How did it come about that..."
Yes, you can use it with sentences containing auxiliary verbs. It's OK with modals as well:
How come you must do your homework tonight, when you don't have school tomorrow?
Note that subject-auxiliary inversion is not required, maybe because what follows is treated as a that-clause (see the comment about a possible abbreviation in the first paragraph). Other than that, your sentences are both OK.
How come you are sitting here when they're all vacationing?
How come you can sit idle when your friends are playing soccer outside?
"How come" (a common alternant to "why" in informal speech) is best regarded as a compound interrogative word functioning as an adjunct in clause structure.
Exceptionally for an interrogative, it doesn't trigger subject-auxiliary inversion, thus
How come you are sitting here ...
is the correct structure.
The idiom "how come" derives from a construction where "come" is a verb taking a clausal subject (cf. How does it come to be that you are sitting here?).
