As a longtime armchair attorney who has closely read summaries of cases like this on Slashdot for well over the past decade (IANAL, BTW)...you could go the lawyer route but this basically amounts to your kid being a minor in school which means they don't have full legal rights, and the interpretation of 4A is likely up in the air here anyway. Constitutional rights don't necessarily apply at school or anywhere near sc…
IANAL, either. Just because the student is a minor, I don't see how that gives the school the right to pwn a private laptop (were the laptop a school laptop, my opinion would be different here); at best, this would seem to be the parent's machine, or right to decide, at that point.
The OP's post isn't very clear on how the school managed to get into a private laptop in the first place; he mentions they "logged on", but onto what? And how does signing into something permit installs? (There's a comment below that hypothesizes this might be an MDM profile sort of situation, and that's … trickier. But doesn't even an MDM login have an uninstall of some sort? (Although, IDK, perhaps Chromebooks just can't do that, but that would seem to be an issue then with their software. But I've never tried, as I don't usually go for MDM stuff myself, as companies that do it typically want too much permission onto what is my personal device.))