The judge accepted a claim at face value that the children in question were “natural-born citizens,” but they were not treated as natural-born citizens. IOW, the judicial “actions” speak louder than the plaintiff’s words. Had this been Barak Sr. suing to extend his temporary visa because of an alleged hardship through his family, the judge would have denied it with the assumption that Barak Sr. would take SAD and Barry back to Kenya, with no reservations expressed. It makes sense that Mrs. Obama filed for divorce when she did, to make sure she didn’t go down with the ship.
Wrong. The courts have consistently held (I looked back from current to the 1970’s and 80’s) that the citizenship of the child did not affect deportation of the parent. The children, as ydoucare pointed out, are free to stay in the United States. So yes, they were treated as natural born citizens. The fact that most families will want to stay together and thus the children will stay with the parent is not relevant to the law.
I give you an analogous case: A woman born in the US, whose parents were also born in the US, marries a foreigner who overstays his student visa. He gets deported. She has the choice to go with him, or to stay in the US without him. She is obviously natural born by your definition, but has the same situation as the children we’re discussing.
And we are discussing the law, whatever some on this thread may want to make it about instead.