Isn't Enishi, Shien's Chancellor suppose to be able to trigger on your opponent's turn? I think it is coded at the moment as an effect that you have to trigger only on your turn play.
Cannot be Normal Summoned or Set. Must be Special Summoned (from your hand) by banishing 2 "Six Samurai" monsters from your Graveyard, and cannot be Special Summoned by other ways. Once per turn: You can target 1 face-up monster; destroy that target. This card cannot declare an attack the turn you activate this effect.
First, the effect of Shien's Chancellor is NOT a trigger effect but an ignition effect, so it's CAN'T be triggered.
Second, what word in the card text makes you think that effect of Shien's Chancellor could be activated during your opponent's turn?
A monster's effect which can be activated during your opponent's turn is a QUICK effect, and a Quick effect must has the word "Quick effect" or "during either player's turn" in its text.