You need to tell your second install to use the port numbers in the web.config file. This way it retains the port number when you click stuff like login. I think you'll then be able to get in and add aliases to your second install, along with that you could do a little NAT/PAT on your firewall and see your second site via the internet.
First thing though is, on the duplicate site, open web.config and find these two lines:
<!-- set UsePortNumber to true to preserve the port number if you're using a port number other than 80 (the standard)
<add key="UsePortNumber" value="true" /> -->
Change it to this:
<!-- set UsePortNumber to true to preserve the port number if you're using a port number other than 80 (the standard) -->
<add key="UsePortNumber" value="true" />
All I did was move the --> from the end up to the end of the text line, thus making the line <add key="UsePortNumber" value="true"/>
this will make the port numbers active on all the things you click on the site. What is happening is you are currently seeing the first page of your dup site, but then when you click something it's kinda redirecting back to the original, non-port number site.
Once that is done it should work, if not, I'd go to yoru primary install, add localhost:portnumber to the alias list, then copy the install to your test install again, and edit the test installs web.config as mentioned above.
Let me know if that works!
Josh