I have no idea how school/board/us/system/it/student thing works so I won't speak to 'how do I get rid of spyware' and 'can I call the police'. It is improbable you can. Like, where I work, if I want to use my work mail with my android phone, my IT mandates I have a remote-wipe installed ... I am hopeful, that the androids work profile keeps the work-it separate from my personal browser history, but I can live with it.
What I would do, is give my kid their own google account. I assume they don't need 'shool-mamaged-chromebook', just 'a computer that can access Google Classroom'. Then, after running the chromebook with your own account, your kid should still be able to log in with the school account in browser, without handing over admin privileges.