Since I'm not familiar with your setup and installations - allow my to ask/mention this:
1) Remote-ness of your external MySQL databases
Are the remote MySQL DBs on the same *DB server* as your WordPress installation?
2) If not - make sure to grant these remote MySQL DBs "remote access" privileges.
This can be done often via the hosting panel. Example: http://www.liquidweb.com/kb/enable-remote-mysql-connections-in-cpanel/
3) WP operates with the $wpdb object using the data provided in the wp-config.php of the WP installation
In order to get data from another WP database but using all WP functionality you need to register another $wpdb object. Like this -> http://wordpress.stackexchange.com/questions/1604/using-wpdb-to-connect-to-a-separate-database
Hope this helps a little bit :-)