How do I have a calendar event schedule to the day rather than date - like the third Tuesday instead of the 17th?

You can't. Suggest it to Apple here: www.apple.com/feedback/

Unfortuneately, there's no way to do that directly on iOS Calendar, which has fairly limited functionality. It can be done on computer calendar apps such as iCal or Outlook and synced to your Calendar on the phone.

The only workaround I know is to create the event on iCal in your Mac and then sync it to your iphone or ipad. Hope that helps you!

If you are a subscriber, iCloud gives you this flexibility. Then sync your phone to iCloud, and the recurring appointment is scheduled on your iOS 6 phone. AppleCare helped me figure this out today.