Wong Kim Ark is the closest the Supreme Court has come to defining 'natural born' and unless and until something is decided otherwise it is the supreme law of the land. You may wish otherwise: get over it. As set forth in Wiki but the money quote is the direct quote from the Supreme Court:

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* United States v. Wong Kim Ark, 169 U.S. 649 (1898): In this case, the majority of the Court held that a child born in U.S. territory to parents who were subjects of the emperor of China and who were not eligible for U.S. citizenship, but who had “a permanent domicile and residence in the United States, and are there carrying on business, and are not employed in any diplomatic or official capacity under the emperor of China” was a U.S. Citizen.

The Court stated that:

The constitution nowhere defines the meaning of these words [citizen and natural born citizen], either by way of inclusion or of exclusion, except in so far as this is done by the affirmative declaration that 'all persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States.'[17]

Since there was no definition of "natural born citizen" found in the constitution, the majority adopted the common law of England that was a carry over from feudal times.

The court ruled:

It thus clearly appears that by the law of England for the last three centuries, beginning before the settlement of this country, and continuing to the present day, aliens, while residing in the dominions possessed by the crown of England, were within the allegiance, the obedience, the faith or loyalty, the protection, the power, and the jurisdiction of the English sovereign; and therefore every child born in England of alien parents was a natural-born subject, unless the child of an ambassador or other diplomatic agent of a foreign state, or of an alien enemy in hostile occupation of the place where the child was born. III. The same rule was in force in all the English colonies upon this continent down to the time of the Declaration of Independence, and in the United States afterwards, and continued to prevail under the constitution as originally established."

The majority did not adopt the dissenters claim that 'under the jurisdiction' meant that no allegiance was 'owed' to a foreign government implying that whatever the laws of a foreign jurisdiction might seek, what was important was that the United States had jurisdiction over persons lawfully here and not subject to diplomatic immunity.

As to allegiance, a child born in this country with dual nationality taken from this country as a small child to other nation in which he has citizenship, the test is whether or not that child on its majority returns to reside in this country and assume the duties of citizenship. Obama has met this test outstandingly. See Elg.