Crossdressing event? And her father is gonna realize something is up when he sees Karou looking like normal (as in Crossdressing) wondering why "she" isn't dressed as a guy?
I find that most secrets authors try to hide aren't worth it. The exception is if the entire story is built around it in the first place. In which case it might still fall flat, but it has a higher chance of success.
Calling it now, asshat from previous school visits and ChadDad™️ puts the fear of Azathoth in him.
Or better yet, Kaoru does (somehow), and ChadDad™️ sees him do it.