I don't think the issue is with going home for Pesach - most girls go home for Pesach, but going home for a Bar-MItzva is somewhat unusual. The principle merely decided it is ok for her to go for that if she compensates by staying for Pesach.
Either I'm missing something (which is possible), or you are.
I understand his new decision/policy is that she cannot go for both. However, the tix were purchased when his old decision was in effect, i.e. she
was allowed to go for both. My point is the girl shouldn't
have to "compensate" by staying for one or the other because the parents detrimentally relied on the school's prior policy (which I'm assuming was communicated in some way to the parents).
Ultimately, though, it doesn't really matter unless the school will kick her out if she goes home for both (which, again, would be ridiculous, IMHO). If not, its simply and ultimately up to only the parents and the daughter whether she comes home for both or not, accounting both for financial as well as spritual aspects.