This does not sound correct.
I can't offer any suggestions as to why one machine is showing twice on the connect to computers web page.
Are any of your machines Home Premium rather than Professional or higher?
As remote connections cannot be made to a standard Home Premium install, it is probably reasonable that they do not show in the connect web page. I am unable to test this as I have replaced my only Home premium install with a Pro version.
Dave
The Frog on the Lilypad at Home