If you set your session cookie domain to start with a "." character it will let you handle wildcard sub-domains and share a session cookie (login session) across multiple subdomains.
In settings.py:
SESSION_COOKIE_DOMAIN=".stackoverflow.com"
The above would allow a cookie to be shared across user1.stackoverflow.com and user2.stackoverflow.com.
If you really do want the url's to be different for the same site, would you want the same user to switch between the two sites on one login session? Or do you just want the ability to have two different users login to the site from two different url's (that are not sub-domains?)