Obviously some information available on your LAN is being balocked with your VPN. I have never worked with a local network via a VPN so perhaps there is a workaround within your VPN software/provider?

Although possibly the easiest solution would be to add an entry to the hosts file on the PC(s) that you want to use to access the Wiki

It most likely is to do with your VPN config (or perhaps limitations of your VPN). Somewhere along the line your hostname is getting blocked. You may be able to tweak it so it works? But I wouldn't know where to start there...

So editing hosts might be the safest, most likely to be successful way (although probably the most tedious). It will need to be done on EVERY PC that will be offsite and connecting via VPS. You would need to add an entry to the host file on each computer. The process for that will depend on the OS. Google will help you out there (google something like "how to edit hosts win7" assuming Windows 7). To clarify, it will only need to be done once per computer but on every computer... You will also need to make sure that your server IP is static otherwise it might change (you can do this on TKL from the ConfConsole).

Another thing might be to set up a local DNS which might be a better option (or add a new entry for your Wiki if you have one already). It will mean just config in one place, however whether that works or not I can't guarantee, again it will depend on your network and/or your VPN...