Domain Setup Question

[X-Dimension]

For security reason i want to use our Zimbra server only in the LAN but i also want to use an external mail server as a relay to send and receive mails to/from the outside. I'm using fetchmail to get all the mails from our ISP and send mails with the ISP as mail relay.

My ISPs domain name is "external.com", the mx record of this domain is "mail.external.com".
The Zimbra server in the LAN has the name "mail.internal.local" with an mx record "mail.internal.local" on the DNS server in the LAN. In Zimbras admin interface i also set the domain name "internal.local".

But with this setup every user has two mail addresses "user@internal.local" and also a personality "external" with "user@external.com" and this is very tricky to handle it.

Can i set in Zimbras admin interface a domain called "external.com" to have only one e-mail address per user or did i get a conflict with my ISPs mail server because im using the same domain name on Zimbra in my LAN?
The name of the mx record in the LAN stays mail.internal.local, only the domain should be set to "external.com" in Zimbra.

Is it possible?