When a card that has been played via Prince is schemed, the game should ask if the Prince set aside effect or the Scheme topdeck effect should occur (or maybe not, the new wording of Scheme makes it sound as if it takes precedence). But obviously, only one effect can happen, the other will loose track of the card.
But what actually happens is that the Scheme topdeck effect occurs, but Prince doesn't loose track, playing the card next turn anyway. For example, load game #9324410 as Inigx. In turn 8 Ingix Princed a Hamlet, which got played normally at the start of Ingix' turn 9. Then a Scheme was played. That's the situation at the last decision of that game.
If the turn is ended and the Hamlet gets Schemed, then Scheme will topdeck the card and Ingix will draw it during the draw phase. After Lord Rat has had his turn, the Prince will automatically play the Hamlet out of Ingix' hand on his turn 10! I don't think that's correct.