Wel, according the Constitution (Article II, Sec. 4) says "The President, Vice President and all civil Officers of the United States, shall be removed from Office on Impeachment for, and Conviction of, Treason, Bribery, or other high Crimes and Misdemeanors.
(Sitting judges are considered civil officers of the United States.)
The question then is, is "...citing international law and custom and not our Constitution" either a high Crime or Misdemeanor?
It is if you have sworn to protect and defend our constitution, and then seek other sources to undermine the same constitution, and then declaring that constitution to be unconstitutional.