How to setup a Remote Connection to MySQL

I have a very large database, so large in fact that my shared hosting plan will not let me upload/import the backup sql file needed to populate the database. The file is 17,584,460 bytes and even zipped its too big for their limits. So what I want to do is place my database on another server (dedicated) and serve it up to my shared host. I am familiar with MySQLs Grant Privileges. I would just like some help on getting this issue resolved. I need to know what command to issue the MySql monitor... Lets say my dedicated server has an IP of [login to view URL] and that is where the MySQL database is residing. But my website is hosted on a shared server... by pinging my domain name I see that my sites IP is [login to view URL] but that is just the shared IP of the server my domain is being served from.. Should I get a dedicated IP for this hosted website to make this connection work? (NOT Actual IPs.. Used for examples purposes only I would like to step by step instruction or advice! Thank You!