Yes, I thought I should draw a picture.
3 + the user
The user will connect to a public webserver with a public IP
the user will need to click a link there that will take them to the proxy server, which has a public IP as well (entirely different physical location)
that proxy server will connect to the other site they need to use
The last one is also publicly accessible but will only let them log in from the proxy server. The difference between this and a regular proxy server is that we can't really have the user configure anything on their end.
I'm on my way out, so here is a very very rough diagram.
The main webserver will contain nothing but a link, so I don't think much has to be done there, I just need to figure out which software to run on the proxy server that will server up the content from the other machine seamlessly.