If DNS lookups are being handled by your Mac Mini Server, and the server domain name is the same as your website, then one option will be to setup Split-Horizon DNS. Not the easiest thing to do, but I am not a DNS wizard. Have a look at this document. There might be something here for you to work with.
I'm going to guess that you have a gateway firewall around, that you have your DNS set to return the public IP address for your server, and that your gateway-firewall box doesn't "reflect" requests sent to your external IP address back into your network. That's more guesses than I'd prefer to make, but...
Details on your particular DNS services and network setup, please?