For external clients (such as Hotmail) when they resolve your MX record, they will need to see your external/public IP.
Originally Posted by responding
Internally on your Zimbra machine, I believe that it can resolve either IP and be fine... as long as it knows that mail meant for itself (internal to the domain) just stays.
It sounds like the problem is that it doesn't know how to send mail out to other hosts ("No route to host"). Try a few things here:
First, on your Zimbra host, run:
For me, it returns mx1.hotmail.com through mx4.hotmail.com as possible mail exchangers for the domain hotmail.com.
If that works out, try:
Which will connect to port 25 of mx1.hotmail.com. It should respond and say something like:
telnet mx1.hotmail.com 25
You can just type in QUIT to disconnect from their server.
220 bay0-mc10-f14.bay0.hotmail.com ........
Your mail server will in essense do the same thing when it tries to send mail to an external server. It'll look up the mail exchanger (MX) records for the server and then connect to the SMTP port (25) and try and send the mail.
So, if you can do both of those manually from your Zimbra host, Zimbra should be able to do them as well. Otherwise, we have another problem. Hope this helps.