Yes, you already can. Asumming you've already set up an MCGalaxy instance on your PC and the computer is running in LAN behind a router:
1. Set verify-names parameter from true to false in properties/server.properties file;
2. Whitelist the port MCGalaxy uses in the firewall of your operating system. Tutorial for Windows. Don't confuse this procedure with port forwarding (which is not needed in your case) and remember that the server uses TCP protocol;
3. Learn IPv4 address of your computer. This could be done via your router or the operating system. Tutorial for Windows;
4. Offer your relative to go into the Direct Connect screen and use that address for connecting. Make sure they are connected to the same network as your PC.
This should work fine even if there is no access to Internet.