How to use VPN with OS X Server?
OSX Server does have several VPN servers in it.
You can configure these using Server.app however, if your internal name resolution is broken this is likely to be more trouble.

You'll also need to make sure your Mac Mini's VPN port is available to the internet on a static IP (or dynamic host name).

As an interim step I suggest looking at 'Back To My Mac' which is free as part of iCloud. Technically it uses adhoc ipsec vpn tunnels and gives you an DNS name for each mac set up, effectively bypassing the current internal name resolution issue. e.g. server.12345678.members.btmm.icloud.com
Services that you run e.g. web and ssh will accessible.

They're btmm DNS address are not internet routable and don't, generally, require any port forward or static IP addresses. 
For a couple more technical details check here: https://apple.stackexchange.com/a/53776/46039