I do not want to get too technical with you, but it does not work that way. You need personal jurisdiction over someone to enter a valid order against them, and I do not see how a court in any other state can gain such jurisdiction over a Hawaii official. There is then nothing to appeal.
And, yes, I am a lawyer - practicing for 35 years.
The State of Washington has personal jurisdiction over Obama. The birth certificate information is relevant to the matter at hand.
In any event, the WA SC can order the Sec. of State to comply with the law to require that Obama prove he is qualified. While a subpoena of his birth records would be best, the petition for a writ of mandamus is to require the SoS to obtain the info regarding Obama’s BC.
If HI can’t be required to produce it, the state can require Obama to do so.