I'm pretty sure it's the guard that wants to. At best the King would take the daughter as a hostage so the guy should stay
But didn't the emperor say "anyone related to hyung must die" after the guard mentioned killing the daughter? To me it reads like the guard understood the assignment. Here's to hoping the emperor changes his mind for real
Or typically force the Doctor to be with him by threatening to harm his daughter. That usually what these red flags tops would do
He's gonna have his family killed, even his daughter? Come on now. There's no coming back from that even if you are a yandere seme