@TheGodEmperor
He mentioned in a previous chapter that the only reason he’s keeping the Duchy and his title is so he can prevent his kids from going through what he did, so that’s why he’s trying to fight this issue legally so that they can just return in peace.
Also, even if he just kills everyone, the public won’t accept a murder of who they assume to be innocent and righteous. The prince covers up the incompetence of the King, so the masses wouldn’t really know that he’s just lazing around. And the prince has maintained a solid facade, it seems.