Scenario #1
The standing is children's rights to both a mother and father in marriage. The case is that they were barred from representation at a contract revision whose end result was to enact provisions that cause a detriment to themselves in a legally-binding way. Which is not allowed when children are at the end of that whip. Consult the Infant Doctrine and contracts for details.
Scenario #2
Judge Moore of Alabama is held to the fire and he appeals all the way to the USSC on behalf of himself and his state. Or the AG of any state joins him. The standing is his defense of his actions with respect to abiding by or not abiding by Obergefell. The case is any number of things, including scenario #1 and Alabama's obligation to look out for its children. But let's say the case here could be that two Justices were not impartial. They displayed bias well before the case was heard. And they did so publicly. The case law supporting is Capterton v Massey Coal (2009 USSC) where the broad understanding there is that nobody sitting in judgment of a case may display bias without recusing themselves..
Scenario #3
A polygamist (polyamorist) group wishes to marry but are barred when they apply for a license. There's the standing: discrimination based on sexual orientation. The case is that because on pages 7-8 in Obergefell, it says the case was about sexual orientation, and the larger scope was that states cannot discriminate based on sexual orientation (therefore). The polygamists challenge that both homosexuality and polyamory were repugnant to the majority. Yet just one of them gets special privilege to marry while the other doesn't. The 14th demands all sexual orientations repugnant to the majority may marry. Not just some.
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Scenario #3 would end with the Court reluctantly telling all 50 states that polygamists, incest and any other conceivable adult combination of sexual orientation must be allowed to marry (and involve children). Because marrying comes with several perks that also cannot be denied arbitrarily. One of those is the right to adopt.
So children ARE intimately involved in this issue of law. And I believe because of them, the Cour will have to instead overturn Obergefell because it will realize its mistake of allowing just some of their favorite, but not other repugnant sexual orientations to marry. Obergefell will implode right before our eyes.