One of the most common mistakes that folks make, is when they want to send email to a domain on another server, when they have that same domain setup in their account here.
What will happen is that the email will be routed locally to the domain on the server, and will not make it off the server at all. If you want to send mail to a domain that lives on another server, and you have currently setup that same domain on this server, then you will need to delete the domain on this server, before the mail can get off this server.
Send in a request to the help desk to delete the domain on this server, so you can send to that same domain, on an outside server.