First, network them if they're not already. (This could be a LAN or it could be anywhere over the internet, as long as they're both on at the same time.) Then decide which Mac you want to be the client and which you want to be the server. The server's drive will show up on the client's desktop.
On the server Mac, go to System Preferences -> Sharing and turn on Personal File Sharing. On the client Mac, from the Finder's Go menu, click Connect To Server and enter the IP address of the server. (Found by opening Applications -> Utilities -> Network Utility on the server Mac)
On the client Mac, you will need to log into the server Mac using a username/password of an account that is present on the server. So that would either be your dad's account, or else create a new account for your remote login on the mini. Each account gets its own home folder and is locked out of all the other home folders (except for the Shared -> Drop Box folder in every home folder). It is possible to change this if you want but you'd have to adjust some permissions.