OK, I think I understand how your VNC works but I don't know how that would work with PC Anywhere. This process of PCA is a direct analog modem to analog modem connection.
For a PCA connection, My "Remote" PC's modem has to dial the telephone connected to the "Host" PC. PCA answers the call within the preset number of rings and loads an interface to allow me to run the clients computer as if I was sitting in front of it. IE: I have their desktop reflected in a window on my computer.
When I finish the session I "End remote control", my PC disconnects the telephone connection and their PC awaits another PCA call. There is never any TCP/IP information exchanged and no browser is ever used.
PCA can be set to run over TCP/IP as long as the "host" pc has a static IP exposed to the internet. To connection via TCP/IP uses ports 5631 and 5632 and the "Hosts" IP address must be set on the "remote" PC to provide connectivity.
I may be missing something in understanding how your VNC program works. What type of connection do you make and if you are calling your system at home via telephone where do you get an IP address?
I'm still confused???