Frankly, the reason she doesn’t discuss Vattel is because Vattel is, ultimately, irrelevant to the discussion. I keep seeing people throw Vattel’s name around, but they miss the point that Vattel himself later said that the natural law definition of “natural born” can be, and is, overriden whenever a nation enacts some form of positive law (which would include, for purposes of this discussion, English common law) to that effect. Because the Framers intended the common law to be controlling for what an NBC is, Vattel’s “natural law” definition is nothing more than an historical curiosity.
The Founders read Vattel in the French original form and utilized his ideas and concepts extensively. They chose his interpretations over English common law in many instances.
The Founders quoted Vattel's treatise to each other and went back and rewrote the section on qualifications for the Presidency specifically to address the issue of Natural born citizen as defined by Vattel. The Founders and the early Congress specifically revised the Immigration act of 1790 in 1795 to codify that American law differed English common law and to protect from an American President who could be claimed as an English subject.