Another alternative, which requires extra resources but much easier to setup, is to use mod_proxy + mod_rewrite on your external Apache. The only requirement is that, as long as the local (internal) IP of www.hypothesisTV.pt can talk to myintranetPC.hypotheticTV.pt.
Your internal web server can even be running IIS.
Your external web server MUST be able to resolve myintranetpc.hypothetictv.pt either via /etc/hosts (easier) or a valid DNS entry (split horizon in your case).
If you have further questions on this, start a new thread in Apache forum.