If you are opening the chat in a new tab/window with target="_blank", you don't need an extra button to "go back". The visitor would just close the chat tab/window when they are finished, and the original page they were on should still be there, open.
As far as minimizing the original page, that would most likely be something in the visitor's control, through their browser settings (maybe with plugins). I know my Firefox gives me the option to open new tabs from links in either the foreground or background (I usually prefer the background, though). Different browsers handle this kind of stuff differently, but it's usually up to the user how they want to configure it in their settings, and even if you have a choice on how to do it on your site, these user settings would over-ride that.
added to your link could set the size, position, and other parameters of a new window, but in my browser, it would never be a new window (only a new tab) and never be the size you set (just a full page), and never open in the foreground (always in the background) because my browser is configured to always do that instead of what the web designer may have intended.
Does this make any sense to you?
One thing that I may not be making clear is that this IS a site where they would probably want the chat on every page. that is the whole purpose of it is to discuss the merits of specific documents and it is a committee of people who will be there and Only them.
I guess the misunderstanding is my fault, because I didn't explain why, from a webmaster's point of view, you wouldn't want it on every page.
Unlike the designer's point of view where this might be a good thing for users, from a webmaster's point of view it's bad because it hammers the server whenever a page gets loaded. Get a bunch of people on the site at the same time, who have no intention of chatting, and if the chat loads on every page you are hammering the server for no reason. There comes a point where you cross a threshold where the number of users on the site is capable of bringing the whole site down, if they are all loading a live chat room for no reason, at the same time (this is why most web hosts don't allow live chat rooms and suspend the accounts of any webmaster that breaks this rule, as it can affect other sites hosted on the same server.). Putting the chat on its own page, to be used only if the user wants to chat, lessens the risk of bringing down the whole site.
But if you still want it on every page, I probably will have time this weekend to help you do it, one-on-one (privately), hands-on, even just doing it for you, if it wouldn't compromise any sort of confidentiality agreement you have with the site owners. Send me a PM by Friday night if you are interested in that kind of help.