They didn't ignore it. They don't agree that Vattel is such a principle:
"The Plaintiffs do not mention the above United States Supreme Court authority [Wong Kim Ark] in their complaint or brief; they primarily rely instead on an eighteenth century treatise [de Vattel] and quotations of Members of Congress made during the nineteenth century. To the extent that these authorities conflict with the United States Supreme Court‟s interpretation of what it means to be a natural born citizen, we believe that the Plaintiffs‟ arguments fall under the category of conclusory, non-factual assertions or legal conclusions that we need not accept as true when reviewing the grant of a motion to dismiss for failure to state a claim. Irish, 864 N.E.2d at 1120"
What a laugh! The Law of Nations written by Vattel is mentioned in the U.S.Constitution more than once - go ahead, read the document yourself.
No where, to my knowledge, is English Common Law EVER mentioned in the U.S.Constitution, and for good reason. English Common Law dealt with the relationship between a sovereign and subjects. The U.S.Constitution deals with the limits of government power over citizens, who ARE sovereign. The difference is awesome.