I'm aware of Vattel, and you are correct on this point.
Vattel is considered the common law source
Here you are incorrect. Vattel is not writing in the Anglo-Saxon common law tradition, but in the continental European legal tradition, which is based on Roman law. US law is based on Anglo-Saxon common law, whose definition of natural born subject/citizen does not require two citizen parents. Hence whatever Vattel says on the matter is irrelevant.
"In common law, a natural born subject could have two alien parents," is complete poppycock.
No it's not, it's based English common law precedent that goes back to the middle ages, much of which is referenced in the Wong Kim Ark decision. Mr. Rogers has already provided the relevant citations, so I will not reproduce them here.
I'm aware of Vattel, and you are correct on this point.
Actually, not quite. Vattel did not use the word "two." You'd think if it were that important, he would have put it in; but, in fact, he didn't. I believe him to be using the same construction as when one says "boys whose fathers played football are more likely to take up the sport;" or, as in Blackstone, "all children, born out of the kings ligeance, whose fathers were natural-born subjects, are now natural-born subjects themselves." I don't think either of those statements means they only apply to children with two fathers, so I don't see why Vattel's statement has to mean two citizens. Like I said, if he meant two, he could have said two.