Ok, it seems you are trying everything :-). Lets suppose your server hostname is hostname.local. If I understand correctly, you are able to access admin. console (ADC) via http://hostname.local/Avast from the computer the console is installed on, but unable to access the same URL from any other remote computer, am I right?

Yes correct.

when accessing from the remote PC, do you see something similar? I'm interested in that Technical details part which lists the reason of rejection. The problem with self-signed certificates is that you have to manually validate (confirm) them. But obviously, you don't have the option to manually confirm the cert (Add exception, in terms of Firefox) and access the site. And we have to find why :-).

Nope, there is no confirmation about accept certificates.