Error forwarding Internal system emails when email is hosted by 3rd party

[elemental.tm]

Hi,

I have searched the forums but I haven't been able to confidently match my issue with anything already documented.
I have the following problem of not receiving email to mydomain.com when initiated from the Plesk Control Panel or from Websites on my server using PHP Mail.

mydomain.com

• Web hosing on my server
• Email for mydomain.com hosted on Google Mail (inc. [email protected])
• Mail service disabled in Plesk
• Bind (DNS) not installed

anotherdomain.com

• Web hosting on my server
• Email for anotherdomain.com hosted on my server
• An email forward exists for [email protected] to forward to [email protected]

Any help would be much appreciated.