The CMS product works just as it is intended. It is your host, Host Gator. Host Gator does not allow for remote connection without authorization. they have two layers of security for MySQL.
The first is going to be that they have the MySQL port of 3306 blocked by their system's firewall and that MySQL itself is set to not allow remote connections. contact their support. You just simply need the IP that you are connecting from and they can whitelist your IP past the firewall. You can obtain this IP by going to ip.shtml
The next step, in cPanel you would just go to "Remote MySQL" and then you can add your IP to the allowed list for connection.
See Host Gator support for complete details