Yes, Obama’s father was not a U.S. citizen. There is no requirement that EITHER parent be a citizen for someone to be natural born. (see US vs Wong Kim Ark)
Yes, the Constitution calls for a “natural born citizen” to be either President or Vice President; and according to the law, if 0bama was born in Hawaii he is a natural born citizen.
The “wrench” is of your own imagining. As you admitted “Other nations citizenship statues have NOTHING to do if one is a U.S. citizen at birth or not”.
I know both the argument, and the prescibed solution. The solution was that only no ‘johnny come lately’ could come to the US and rise to the highest office in the land. Only someone who was a U.S. citizen from birth could hold that office.
see US vs Wong Kim Ark
please show me where in that case it discusses Natural Born Citizen.