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.
The card doesn't say "During either player's turn", so you can only use it during YOUR Main Phase. A trigger effect can only be activated if its condition was fulfilled like "if this card is destroyed and sent to the GY" or "When this card is Normal Summoned", etc.
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.