Other than several Supreme Court decisions that specifically use Vattel's definiton and go so far as to characterize it as the "nomenclature of which the framers of the Constitution were familiar ..."
The phrase you use referred not to Vattel, but to the common law. And whenever the Court says “the common law,” that includes the English common law which was our heritage.
It’s the same common law that the Wong Court referred to repeatedly, over dozens of pages.
The remedy for a bad President is to scratch and claw at the bad President, not to scratch and claw at our Constitution.