nothing special needed at all, we have 6 BES on the same network.
it does sound like a permissions issue, are both BES running using the same service account ?
This is bad: "BesAdmin has full permissions over the whole domain."
the account should be a regular user in the domain with some local admin on the BES server and special perms into Exchange.
Have a read of this for some more help: Users cannot send e-mail messages from a mobile device or from a shared mailbox in Exchange 2000 Server and in Exchange Server 2003