Can't comment much on web-based chat, other than I tried it once or twice somewhere, long ago, and found it not to my liking.
It is not often that I use/need internet relay chat, but when I do, I use mIRC. It is Windows shareware that works fine for free. You might want to grab a copy and install it, assuming you use Windows.
Server for ADT is irc.adultdvdtalk.com . Port is 6667. After connecting, join #adt . That's the basic info needed to use mIRC for the ADT chat.
For those that don't use Windows, there are irc client programs for other operating systems.
there's no reason you can't go through a proxy with irc, a quick search shows a bunch of free ones and programs to do it for you. i can't recommend any specific one, but they all should do the same thing.