If you ever send mail from any site that is on the same server where your site is hosted, your external mail server will not receive the mail.
The reason for this is that a server will always try to send locally before it tries what the actual DNS or MX zone points to.
The way to fix this is to e-mail email@example.com saying "Please remove my domain ****.com from /etc/localdomains and add it to /etc/remotedomains".
Only we are able to make this change for you. Once the change is done, the problem should be fixed.