your host should have access to the MySQL server from the control using phpMyAdmin.
when you connect to the database using phpMyAmin, it will show the host name in the upper left hand corner, use that host name in the database connection.
Also, double check the testing server settings in your site definition, since you are trying to connect to the remote database, make sure the testing server settings are set to connect to the remote server through FTP and that the web URL is set correctly.
Keep in mind that DW connects to the database by uploading a file to the testing server and using the web URL in the testing server settings to access that file. so the connection is really being made through the testing server and the results then sent back to DW.