I think you need to read the case a bit more carefully. The opinion, by Thompson, J., specifically says:
"How then is his father Charles Inglis to be considered? Was he an American citizen? He was here at the time of the declaration of independence, and prima facie may be deemed to have become thereby an American citizen. But this prima facie presumption may be rebutted; otherwise there is no force or meaning in the right of election. It surely cannot be said that nothing short of actually removing from the country before the declaration of independence will be received as evidence of the election, and every act that could be done to signify the choice that had been made,
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"except actually withdrawing from the country, was done by Charles Inglis. He resided in the City of New York at the declaration of independence, and remained there until he removed to England a short time before the evacuation of the city by the British in November, 1783; New York during the whole of that time, except from July to September 1776, being in possession, and under the government and control of the British, he taking a part and acting with the British, and was, according to the strong language of the witness, as much a royalist as he himself was, and that no man could be more so. Was Charles Inglis under these circumstances to be considered an American citizen? If being here at the declaration of independence necessarily made him such, under all possible circumstances he was an American citizen. But I apprehend this would be carrying the rule to an extent that never can be sanctioned in a court of justice, and would certainly be going beyond any case as yet decided.
"The facts disclosed in this case, then, lead irresistibly to the conclusion that it was the fixed determination of Charles Inglis the father, at the declaration of independence, to adhere to his native allegiance. And John Inglis the son must be deemed to have followed the condition of his father, and the character of a British subject attached to and fastened on him also, which he has never attempted to throw off by any act disaffirming the choice made for him by his father.
"The case of McIlvaine v. Coxe's Lessee, 4 Cranch 211, which has been relied upon, will not reach this case. The Court in that case recognized fully the right of election, but considered that Mr. Coxe had lost that right by remaining in the State of New Jersey not only after she had declared herself a sovereign state, but after she had passed laws by which she pronounced him to be a member of, and in allegiance to the new government; that by the Act of 4 October, 1776, he became a member of the new society, entitled to the protection of its government. He continued to reside in New Jersey after the passage of this law and until sometime in the year 1777, thereby making his election to become a member of the new government, and the doctrine of allegiance became applicable to his case, which rests on the
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"ground of a mutual compact between the government and the citizen or subject, which it is said cannot be dissolved by either party without the concurrence of the other. It is the tie which binds the governed to their government, in return for the protection which the government affords them. New Jersey, in October, 1776, was in a condition to extend that protection, which Coxe tacitly accepted by remaining there. But that was not the situation of the City of New York; it was in the possession of the British. The government of the State of New York did not extend to it in point of fact.
"The resolutions of the convention of New York of 16 July, 1776, have been relied upon as asserting a claim to the allegiance of all persons residing within the state. But it may well be doubted whether these resolutions reached the case of Charles Inglis. The language is
"`that all persons abiding within the State of New York, and deriving protection from the laws of the same, owe allegiance to the said laws, and are members of the state.'
"Charles Inglis was not, within the reasonable interpretation of this resolution, abiding in the state and owing protection to the laws of the same. He was within the British lines, and under the protection of the British army, manifesting a full determination to continue a British subject. But if it should be admitted that the State of New York had a right to claim the allegiance of Charles Inglis, and did assert that right by the resolution referred to, still the case of McIlvaine v. Coxe does not apply"
Thus the case applied British common law for the reasons stated in the material quoted above, that is to say, because father and son elected to be and stay British subjects.
In point of fact the right of election upon which the case turned, was established in the law of nations as Justice Thompson noted, citing specifically Vattel,and such American authorities as Kent's [he of Columbia law school] Commentaries on American Law, and American cases, where he says:
"This right of election must necessarily exist in all revolutions like ours, and is so well established by adjudged cases that it is entirely unnecessary to enter into an examination of the authorities. The only difficulty that can arise is to determine the time when the election should have been made. Vattel, B. 1, ch. 3, sec. 33; 1 U. S. 1 Dall. 58; 2 U. S. 2 Dall. 234; 20 Johns. 332; 2 Mass. 179, 236, 244, note; 2 Pickering 394; 2 Kent's Com. 49."
You have been extraordinarily selective in choosing a small passage from Snug Harbor, and, in doing so, have distorted and misrepresented its holding. It turned upon a right of election carried into early American law from the law of Nations; English law applied to the Inglises father and son because of the election that they made to be British subjects. So, to sum it up, what I said about what Story held in Shanks is in fact correct. I believe that you failed to carefully read Snug Harbor.
One simple way to demonstrate that you're reading Inglis incorrectly is to observe that in U.S. v. Wong Kim Ark, it was the Court majority of six justices who accepted that Inglis supported the view that our citizenship law follows the English common law rule of jus soli. Inglis was not cited by the dissent, which was urging application of Vattel.
As to Shanks, both sides in WKA cite it, which should signal that the case doesn't clearly favor one birth-citizenship view or the other. Ann Shanks was born in South Carolina before the Declaration of Independence, so the case isn't terribly helpful on the question of what birth-rule held true in the U.S. afterward. It was an international law case involving treaties. Yes, the law of nations has relevance to that. But the opinion doesn't bear out your claim that Story asserted that "the Framers, in matters of citizenship, looked to the law of nations." Story doesn't say one word about the Framers.