for the database side, this is simple.. you will need one of the two systems to see the users table modified to suit the other... we will suggest here that you edit your actual system to follow vBulletin structure, to make it easier to upgrade on later uses.

also, as you require your users to be able to login on both systems, sharing a single cookie is quite simple here, as vBulletin manage cookies in a jar!

this is the usual system we suggest when clients want to install vBulletin on their server... and as an information, PHP is quickly installed on a webserver, it does not take more than 3 minutes, download counted!