The reason why I am defining the database connection info again is due to the fact the database is different to the one I use for vbulletin and which is obviously called from config.php. The server is the same (domain) but the connection info is different due to that factor.
As long as the MySQL user set in config.php has permissions to read your other database, you can do this inside your query (and save yourself starting another connection):
PHP Code:
$vbulletin->db->query_read("
SELECT *
FROM database2.table3.field4
");