I never understand the premise of these fake otome games or stories. In no world, can a prince easily execute or murder a dukes daughter, even if she killed a commoner or low ranking noble. That's basically another Tuesday for a noble. He's the prince, not the king.
Unless the duke has absolutely no political power, it would never happen, since that's essentially the equivalent to starting war and extreme disrespect, and in these stories, the villainess's family is usually still very powerful.