Looking for a module or component that is a calendar with certain features.

I will use a hair salon as an example. I would like people to click on a day, and choose a time for an appointment, probably in half hour or hour intervals.

Then the calendar will update on the site so no one else will try to book that time.

Would also like the owner of the site to be sent an email notification upon appointment.

I have checked everywhere and can't find anything but google calendar which requires connecting with ical or something, and it doesn't seem to fit my needs.