British Common law is not American Common law or has it ever been. We derive origins from British practices, but it is not the same as we are a totally different sovereign.
You have made several statements which seem to have no bearing on my point. British Common Law was a source for much of our Constitution, and courts often go back to it in interpreting American law. So one can’t reasonably claim the Constitution based a particular thing on Vattel, without proof and no one has shown any. There is however, the Madison quote, showing what the “Father of the Constitution” thought about this.