and how does this judge intent to enforce his edict?
He won't have to; the lawyer for the Probate Judge said at the argument in court today that his client (the Probate Judge) didn't care which way the federal court ruled, he just wanted clarity because he didn't know what he was legally required to do.
But if, hypothetically, the Probate Judge were to refuse, the federal judge would hold him in contempt of court and send U.S. Marshals to arrest him. Because this would be civil contempt, not criminal contempt, there would be no jury trial; the federal judge would simply order him held in jail until he agreed to comply.