Thread:Project:Support desk/Cofigure 2X $wgServer/reply

Don't use an IP. Use a domain name. Then configure DNS properly so each network resolves the domain name to the correct IP. That's what you should use when it's being accessed from the Internet and also from the internal network.

Having 2 server names would cause cache fragmentation. If a user on network A saves an edit, it will be saved in parser cache with the server of A, and then, when viewed by user from network B, all links would be pointing to server from A leaving to nowhere.