I have not read every brief/opinion/order to know which ones discuss the Supreme Court’s decision in US v Wong Kim Ark.
If you haven’t read the complete “Natural Born Citizen” section in Ankeny v Daniels, you should. It seems to have made sense to subsequent judges looking into this issue since it keeps being cited over and over.
http://www.in.gov/judiciary/opinions/pdf/11120903.ebb.pdf. [the discussion begins on page ten of the court’s opinion]
I have no knowledge of any lawsuit that has focused on “permanent domicile” as a prerequisite for the child born in the US of alien parents.
However the holding in US v.Wong Kim Ark also notes: [An alien parent’s] “allegiance to the United States is direct and immediate, and, although but local and TEMPORARY, continuing only so long as he remains within our territory, is yet, in the words of Lord Coke in Calvin’s Case, 7 Coke, 6a, ’strong enough to make a natural subject, for, if he hath issue here, that issue is a natural-born subject’”
“Subject’ and ‘citizen’ are, in a degree, convertible terms as applied to natives; and though the term ‘citizen’ seems to be appropriate to republican freemen, yet we are, equally with the inhabitants of all other countries, ’subjects,’ for we are equally bound by allegiance and subjection to the government and law of the land.’
“Subject’ and ‘citizen’ are, in a degree, convertible terms as applied to natives; and though the term ‘citizen’ seems to be appropriate to republican freemen, yet we are, equally with the inhabitants of all other countries, ’subjects,’ for we are equally bound by allegiance and subjection to the government and law of the land.’”
Since Wong Kim Ark’s parents returned to China, never to return to the US, the permanence of their domiciliary status was open to question. The reason that Wong Kim Ark was originally barred from reentry into the United States is because he had gone to China to visit his parents.
According to the facts of the case, it wasn't open to question. Wong Kim Ark's parents were permanently domiciled in the U.S. when their son was born in 1873. They raised him in the U.S. and didn't return to China until 1890. This is a known fact to all parties of the case; the info is contained in the case syllabus. Given that, the parties agreed upon the fact that his parents were permanently domiciled in the U.S. at the time of his birth. Gray specifically states that his ruling is based upon that and the other facts agreed upon by the parties.
Case Syllabus:
U.S. v. Wong Kim Ark - Syllabus
That said, given the information we now have on Hawaii and Alaska being the only two states in which birthright citizenship is not predicated on the "subject to the jurisdiction" requirement, it would appear that if Obama was born in Hawaii as presented, he is a U.S. citizen.
The question that remains, though, is if a born British citizen is a natural born U.S. citizen.
Given our Founding Fathers' break from British alliegance, I am quite sure they never intended such to be the case.