Tougher questions were aimed at Stephen Cullen, attorney for Lynne Chafin, who said "once the doors close on that plane and that child arrives back in Scotland, unless the plane turns round and comes back again, it is all over" on any appeals.
"You're not going to suggest all those countries that permit appeals explicitly and stop removals until appeals are finished, that those contracting treaty parties are breaching the convention, are you?" said Justice Sonia Sotomayor skeptically.
Roberts -- the only justice with young children -- suggested the father was not given a proper time or opportunity to appeal once the initial removal order was signed by the federal judge in Alabama.
"It seems to me," he said, "the best thing is to hold things up briefly, so that the child doesn't go overseas and then have to be brought back, particularly if you have situations where there can be an expeditious appeal. And I think most appellate courts would appreciate the benefit of that."
Justice Stephen Breyer said just because the child is in Scotland, does not mean federal courts in the United States still have no role to play.
"I don't understand why you want a treaty where the best interests of the child are what's at issue, and then you interpret it in a way that the court of one nation with the child where you have parents from both nations pays no attention at all to what courts in other nations are saying."
Jeff Chafin was in the courtroom for the morning arguments, dressed in his Army dress uniform.
"I told my little girl I would do everything I could to get her," Sgt. Chafin told CNN National Correspondent Joe Johns this week, "to make sure she's safe." He last visited the girl overseas a few weeks ago.
"I don't believe that (the current legal fight) is in the best interest of the child as it's going to go on for years and years to come," Lynne Hales Chafin told CNN.
A ruling is due in a few months. The case is Chafin v. Chafin (11-1347).