A Writ of Mandamus issued in Alabama would only compel action by Alabama’s Secretary of State or the lower court in Alabama where this lawsuit originated. How Hawaii would then respond is anyone’s guess.
MY guess is that the Hawaii Registrar would work with the Alabama Secretary of State to craft a remedy that is consistent with the provisions of Hawaii statutes yet meets the requirements of the Writ of Mandamus in Alabama.
That is what happened in responding to eligibility documentation requests from the Secretaries of State in Arizona and in Kansas.
If this was a certified vital record for a normal citizen that would be granted immediately surely?