This thing is driving me crazy

Ok. Forget about Live support. Let's say I don't care about it for the time being.

I want to have a single room which will be accessible by a specific user group.

I have created that room and have assigned access to the desired group.

When I login as a user of that group I'm faced with a public chat room and I have to select the private room.
But since I have only one room defined (private) why am I seeing the public room?
I would like to be joined to the private room automatically since this is the only room available and I have access to it.
This is going to be confusing form my users.

If I disable chat for public at the backend then I cannot choose a room at frontend!

Please let me know how I can achieve the above simple scenario.

Thank you.