We have a small lightweighted applet which establishes a network connection, sends an http request to some server, and receives a reply in xml format.
My project tried to do the same thing: using an applet to connect to some other URL besides the original web server, but we could not. We ended up writing a proxy servlet that would forward the mesages to the other machines. The Servlet has no sandbox issues, so it is free to open connections to anywhere and send messages just like a full-blown Java application. The servlet also ensured that we had no firewall issues since we were always talking to port 80.
Consider writing a Java daemon on some port like 8888, then have that daemon forward the applet messages. It can make connections to anywhere.