E-Mail/E-Mail Server

Sounds like you have a DNS issue. If your e-mail is stored on an external mail server and your internal domain is the same as your mail domain, then your machines probably don't know how to get out to the mail server.

There are a number of ways around this. I personally wouldn't recommend using the same domain internally and externally, but now that you have, the easiest way to fix this particular problem would be to manually add an entry to your DNS server for the external mail server using the external IP address for that server. Your PCs will then be able to resolve the mail server name.

Exactly yoru domain is trying to resolve the address because it thinks it is respionsible. Just make a DNS host entry for the host name of the server with the public IP address of your 3rd party email providor.

You may also find it useful to change the domain name from domainname.extension to domainname.local - that way the network and you are easily able to differentiate between the internal and external networks. If needs be, run a separate DNS Servers for each side of the network - although this is a bit extreme. Also check any MX records as these are specific DNS records for Email. But is definately a DNS issue.