Oh yikes. I know how that goes. I used to work at a restaurant with a bunch of high school kids. You could always tell which ones actually needed the job - they showed initiative and would put in the effort. The others had the privilege of having parents willing to shell out money whenever. Those were the ones who had to constantly be told what to do. As assistant manager, I never fired anyone, but did send people home early from their shifts. No sense in them staying and getting paid for the work the others were putting in.
Sounds like she needed that reality check from you. If she wants to be immature and put in her notice instead of owning her mistake and moving forward, that’s on her. Hopefully she shows up for her last two weeks, though. We had kids who didn’t seem to understand that putting in your two weeks meant that you still had to work for two more weeks... 😐