I'm an employer for 30 years. So I've had my share of people who are truly sick a lot and people who are faking.

You look like someone not paying attention to the people reporting to you. She looks like she has a case of "lazy much." That is a bad combination for the company.

You should have been on top of this earlier. Then it wouldn't have needed to go to the CEO. She'd either be at work more, no longer employed, or no longer your direct report (if her dad has that much pull).