As you mentioned, there cannot be two instances of the chat on the same tab (page) at this time.  We have had a few suggestions from other customers to give the module the ability to have multiple instances on the same tab, but we have not yet integrated this request in the latest release.

However, you are free to put the chatroom on as many different pages as you wish.  You can have many separate instances of chatrooms on different pages.  We have one client who had a similar problem that you face (wanting to be able to have a "side" chat for moderators).  Here's how they setup theirs:

1. Create two tabs (one for 'public' chat, and one for 'moderator' chat).
2. Create a link to the 'public' chat that everyone can see.
3. Create a link to the 'moderator' chat that only admins can see, AND make the link open the window in a NEW window with some javascript.  (if you need help with this part, I can help you.)
4. Now, when a moderator logs in, they open the public chat, and then click the link (which only they can see since they're admins) to pop-up the other 'moderator' chat window. 

Now you essentially have two chat windows running, one public, and one private for moderators only.

Let us know if this helps solve your problem or not, and we'll be happy to help you get the desired effect that you need.

-- Will Gillen
-- Swirlhost Inc.