Setting aside the "Under God" issue, AS REQUESTED, I'll dive right in.
The problem with the SCOTUS decision lies in its reinforcement of non-custodial parents (90%+ fathers) as nothing more than wallets. If, as noted, the father only has his daughter 5.9% of the time, and by extension of the Court's reasoning, he only has 5.9% parental authority, ergo, insufficient standing to bring the action, why is he legally, upon pain of imprisonment and other penalties, responsible to provide for 50%+ of her upbringing? Radical imbalances of authority and responsibility are one of the hallmarks of slavery.
Now, he IS using his daughter to push his agenda. That is a tragic irony, considering that the mother and the State are using his daughter to enslave him.
(note: elements of this posting constitute a polemic.