I also have the family tradition to say Parshas Haman repeated twice and followed by the Aramaic Targum translation. Should that also be repeated on the night after?
A. Indeed some Poskim hold that the tradition of saying Parshas Hamon includes repeating it twice followed by the Targum or Aramaic translation. (Nitei Gavriel , H. Purim !; 3). If you will say it at night as advised on the question above, it should be said on the usual manner.