Have you checked the server config to make sure it is set to allow authenticated users to relay. I think I have run into this before where only local network users will relay. You may also need to use an SMTPSecureSocket as some authentication methods are disallowed over SMTP by default in recent versions.
There are really a lot of config options that could affect this, so if that doesn’t yield any results, you may need to go through the config line by line, or turn on a higher log level to get more info.