The "natural" part of natural born citizen comes from natural law. It does not modify "born," it modifies "citizen." Under natural law, citizenship descends from the father. Under the law at the time the Constitution was ratified, women derived citizenship from their spouses. This was the case right up into the second decade of the twentieth century, when the 19th Amendment was ratified.
Women's citizenship was something of a cause célèbre in women's rights circles at the time, and led to that amendment. You should look into it. Maybe you would find something there that would relieve your angst over having told your children that they could run for President. After all, it's the law at the time the Constitution was ratified, that matters as far as eligibility. Original intent likely only countenanced the citizenship of the father, and took derivative citizenship of the mother as a given. That would mean that you didn't mislead your children. Think about it.
There are native born citizens who are not described as being natural born. Native born clearly refers to those born in the country, and yet it's used interchangeably with natural born in certain contexts. So, natural born means born in the country, and it also means something else, otherwise the distinction would not be made in the Constiutional eligibility clause. There is no other thing that it could mean other than parentage. You've been around these threads long enough to know what that other, additional level of meaning would be ... citizen parents.
Every legal decision that has explicit reference to the term of art "natural born citizen" states that those born in the country of citizen parents are without a doubt natural born, and those that aren't are in doubt. It couldn't be any clearer, and yet here you are, two years later, still sauomg the same things you've been saying all along.
You are correct that it is not in doubt that those born in country of citizen parents are natural born citizens. But that does not follow that ONLY those born in country of citizen parents are natural born citizens. The very argument you are quoting goes on to EXPAND that definition to those born of citizen parents serving their country overseas.
The English law precedent cited in Wong Kim Ark said that even aliens “subject to the jurisdiction” of England when their child was born (excepting only diplomats and such) was a “natural born subject” and extended that same principle to Wong Kim Ark.
So go mislead your own children, how childish.