@Prototype_Xi They aren't giving her a beating just because they feel like it.
She quite literally walked up and insulted in public someone that is basically a supremely powerful king, and the very person she and her father are asking for shelter.
Someone with so much power and authority that her father is giving up his own prince status just to be protected by him.
Someone that the freaking GODS warned to not cross.
And even after a retainer forcefully pointed it out to her she still didn't even apologize.
If she had done the same to another king with a less merciful attitude she would have ended up at least imprisoned, if not EXECUTED.
For the incredibly stupid thing she has done she is getting off LIGHTLY.
They are teaching her that here her arrogant attitude will not be tolerated, and that the people above her have not only the authority but also the sheer power to enforce their will.