Hey Greg, thanks for reaching out!
There might be a couple of ways to go about something like this.
One would be to use a plugin for redirecting URLs. I’ve used Redirection a number of times and it does a nice job of handling alternate URLs.
You can also use a template override to hide information on the calendar from non-logged in users. The process for overriding any of the calendar templates can be found in our Themer’s Guide. From there, I would suggest wrapping private elements with the is_user_logged_in() conditional offered in WordPress.
Do either of those methods sound like they’ll do the trick? Please let me know. 🙂
Cheers,
Geoff