Are both applications Mendix applications? Then I think you'll need a module like Pusher https://docs.mendix.com/appstore/modules/pusher to get events from client to client.

If your backend chat app is something like Drift it's as simple as placing a piece of Javascript on your page layout with the HTMLsnippet widget from the Appstore to get the chat popup, just like a regular helpdesk or sales chatwindow/bot on any other site.

A webinar of last year by Mendix maybe covers some of your questions: https://youtu.be/3-s2ucSq5tw