Creating an event module with repeating dates - but limited registrations per date.

Here's my conundrum...

I need to build a module that allows admins to create events that may have multiple dates. Using appointments as an example, the architecture of the content type may look like this:

Appointment Title
Description
Location
Date 1
Date 1 available slots
Date 2
Date 2 available slots
Date 3
Date 3 available slots
... etc ...

Then, I need a form (calendar?) where a user can select one of the dates (if there is an opening), click it, fill out a form, and once submitted the available slot is removed automatically.

Does anyone have any thoughts on this? It must have been done before, but like so many other people I've searched for hours to find a module (free or pay) that does just what I need.

I'm new to module development, but fairly experienced in drupal/php/ui dev.

How would you approach this type of project?

Cheers!
Andrew