High-level stuff only from me on this sorry - I'm not good with postfix at all.
You want the mail server to be configured as the smarthost and the clients set up to use this mail server as their smarthost.
From memory, you need to put the following config entry into your client postfix config:
relayhost = mailserver.fully.qualified.domain.
I'd suggest making a DNS alias for this (Solaris will automatically use mailhost.localdomain if it exists so I use that name) so if you ever move mailservers, you don't need to update all (I know there's only 2 but if you ever grow...) your clients.