Although not a good practice, the database (if you work with this) and the session configuration, must be the same.
Files: site1/application/config.php, site2/application/config.php
$config['sess_cookie_name'] = 'site_cookie'; // Important! Must be the same name in both sites
$config['sess_expiration'] = 7200;
$config['sess_expire_on_close'] = FALSE;
$config['sess_encrypt_cookie'] = TRUE;
$config['sess_use_database'] = TRUE; // If you work with database
$config['sess_table_name'] = 'sessions'; // Important! Must be the same table
$config['sess_match_ip'] = FALSE;
$config['sess_match_useragent'] = TRUE;
$config['sess_time_to_update'] = 300;
The rest is work with your interface and front-end.