She’s acting like an evil stepmother.

It’s a common trope in movies, TV shows, and books that boarding schools are places that uninterested parents send their kids away to because they don’t want to deal with them. That is undoubtedly an overgeneralization. There are feeder boarding schools throughout the United States where nearly all of the student body get into an Ivy League or equivalent university. I’m sure many loving and caring parents would send their children to a school like that if they had the financial means to do so. Also, it’s notable that most boarding school students do not attend from the ages of 8 to 18. Most of them begin when they’re in high school and are better equipped to emotionally cope with being away from their parents for extended periods of time. Heck, they might even appreciate their relative independence compared to their peers who attend public or private high schools. 

Every comically exaggerated stereotype contains a grain of truth. Bad parents sending their children away to boarding school because they are rejecting their presence does happen, and the damage that comes from it may never be repaired.