Incest is a taboo, regardless of what the Emperor wanted to do with the Empress. The Emperor knew this very well, but not long before the events of the movie, he had only been poisoning the Empress for 10 days prior to the festival. I don't really think it's important that for how long or since when the Emperor start punishing the Empress, but the reason of that was 100% the incestuous relationship with the Crown Prince.
The key moment in the private conversation between the Crown Prince and the Emperor occurred around minute 30. Crown Prince Wan had asked the Emperor twice not to make him the heir, and this should be kept in mind.
Fast forward to minute 45, where the Emperor and the Empress are having a conversation in front of a picture of the previous Empress. This established that the Emperor had been neglecting her after having her carry two children for him. Therefore answering the question of why the Empress has been retaliating this whole time.
Here is the part where I made my assumption: The Empress was completely neglected by the Emperor during the three years of incest, which was during Prince Jai's duty at the border. However, somehow the Empress was still occasionally sexually satisfied. It's not hard to imagine that she had incestuous relations with her first son, as Prince Jai was at the border and the third prince was the Empress's own son. The only one left was the first son.
We can see that the first son was trained in martial arts and other things because he wanted to become the heir at the beginning. It was strange that he suddenly wanted to drop it.
Finally, to confirm all of my assumptions, as well as the answer to the above comment to elaborate on this fact, at minute 68, when the Crown Prince was recovering from a failed suicide attempt, the Emperor told him straight up that he already knew about the relationship between the Crown Prince and the Empress.