Use the stand alone version and modify using the MySQL customization for private users.
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This is the instructions to customize the Ajax chat for a separate login system:
https://github.com/Frug/AJAX-Chat/wiki/Custom-integration-howto
Some things to look into is what database your login system does to, etc. I haven't had a chance yet to look into your login system as I'm on the road.
I assume you have access to view your databases. If you prefer a gui for it, you can use phpmyadmin. You'll need to know the user table and password method to customize it with the software installed.