Can you tell me if this is wrong?

I'd email her back asap and tell her you didn't appreciate her antics, shes probably friends with the girl or something. Say excuse me for wanting to have something done on time and tell her what she did was extremely wrong. As for the other girl the late when apologize for being angry and tell her youd like it as soon as possible. Or just ignore the rude girl in class but don't look away purposely or look scared if she tries to give you dirty looks if thats what you're afraid give them back. But do go to class with an open calm mind to start it off