Just to make a very, very, very clear point.
Vattel’s “Law of Nations”
WAS NOT
the basis of the U.S. Constitution.
Our Constitution was based on English Common Law. It was only in 1938 that the Court abandoned Common Law.
I'm going to expand on this. It doesn't matter if Vattel's Law of Nations influenced the Constitution or not.
1. Vattel's book was not law, is not law, and won't be law unless either SCOTUS incorporates it into law, or it is codified by Congress. It's definition of was "natural born citizen" is does not count for anything. Period. 14th Amendment and the United States v. Wong Kim Ark decision covered it.
2. The Erie case is more complicated than that. It ended federal common law and applied the state common law in federal diversity cases. For non-lawyers here, diversity here refers to cases in federal court due to parties being in different states among a lot of other things that would take a whole semester of civ-pro to understand.