I'm guessing the white haired duke was actually in love with the emperor not the empress

definitely. MC is basically the same as the Duke but gender swapped the love interests (& vice versa). With that one "dream" panel, it seems smth like the MC and the prince actually having shared history which I'm guessing will be another "Changed the course of time to defy fate" or whatever where things go oddly different from the original universe and the world is just waiting for the MC x Prince to happen lmao