Ahhh, the pleasures of shared hosting!
The best thing to do is simply use a different browser for each site whenever you actually require being logged in to both sites simultaneously...
To explain why this is important, you must understand the following, however:
Session
variables are stored on the server, with a keyed reference on the server and a cookie on your browser. Once you unset and destroy either of the two, a match can no longer be made - and your session is gone!
session_start();
session_unset();
session_destroy();
The above will kill all session variables linking the server to your browser (on the server side).
The way to manage this easily is to make session variables into another set of arrays:
$_SESSION["site1"] = array( $user_id, $session_id );
$_SESSION["site2"] = array( $user_id, $session_id );
You could of course make it fancy:
$_SESSION['site3']['userID'] = 'someuserid';
$_SESSION['site3']['sessionid'] = 'somesessionid';
Then when you logout from site 1
session_start();
unset($_SESSION['site1']);
In this case, you have created a separate session management system for each site (using a two-dimensional array, the top layer of which is keyed by your site's identifier). This makes it so that each site manages a separate set of session variables - and when you destroy one, you do not touch the others.
However, I realllllllllly recommend using different browsers instead (or in addition)...