As I said, I’m not going to be drawn into an argument about what the Founding Fathers meant or didn’t mean. I only know what the US Supreme Court decided. They, and I disagree with you and the “Law of Nations.”
Then you also also disagree with G. Washington, John Jay and the Constitutional Convention of 1787. Vattel and the Law of Nations issue was not introduced in those court cases, as they were not explicitely about the “Natural Born Citizen” issue.