It ain’t that simple. You can’t have courts in one place issuing orders that people in other states or other countries have to jump to obey. The plaintiffs in this case could have filed in Hawaii which would be able to compel Hawaiian government officials to do whatever the local court ordered.
Yes, it really is that simply. If HI chooses not to comply, and Obama refuses to provide the documentsa; there is no legal reason preventing the WA SC to grant the petition for a writ of mandamus or declaring that Obama is not qualified.