This is a FAQ and has been answered over and over agein already
OK, so once more:
Cookies are bound to one domain only, so there is no way (without tricks like 1px images to transport cookies) to use one cookie on 2 domains.
To identify a vBulletin user, 2 cookies are important: bbuserid and bbpasword (where bb is a cookie-prefix, .could also be smth. else -> config.php)
Cookie bbuserid should be obvious: this is the userid.
Cookie bbpassword is a bit more complicated. This md5(md5(md5('PlaintextPassword'), salt), 'LicenseNo').
PlaintextPassword is the password, salt the value of column salt (in table user) for this user, LicenseNo is you vBulletin license number.
Column password in table user is md5(md5('PlaintextPassword'), salt).
Does this help you?