The issue is not territorial jurisdiction, it’s political jurisdiction which goes to allegiance.
The woman is a citizen of a foreign nation, i.e., a subject.
Therefore subject to the jurisdiction of the nation that she belongs to.
You are making the same semantic mistake that others do, because the original understanding is not understood now over a century and a half later. Eastman and Meese explain this in their brief in Hamdi.
If the Mexican mom in a Laredo hospital beat her newborn to death, could she be tried for murder in a US court?
Yes!
Therefore she is in US jurisdiction.
If the Mexican mom in a Laredo hospital just slugged her newborn, could the newborn be taken away from her under US law?
Yes!
Therefore the baby is in US jurisdiction.
If the Mexican mom in a Laredo hospital was high on cocaine while delivering, could her ‘coke baby’ be taken away from her under US law?
Yes!
Therefore the baby is in US jurisdiction.
If newborn was the male heir to a $10 billion Mexican fortune, could he be taxed under US law?
Yes!
Therefore the baby is in US jurisdiction.