It's almost a vacation, in a sense.
Come to Mind Control University! Get away from the consequences of your past fuckups and make new, exciting ones! And this time if she screws up too badly, the consequences will almost definitionally fall in someone else's lap.
She's managed to arrange a Regent for while she's away. She could, in theory, just not go back, but her mother didn't raise her to shirk her responsibilities.
The fact that the dorm room she's been assigned at this place is more luxurious than the Dark Lady's suite in the royal palace is a surprise, but a pleasant one. She unpacks (all by herself! With no servants to bother her! Whee!) and then flops on her selected bed, rubbing her neck against the pillows to mark her territory.