If you don't have the password to the current admin account, there'll be no way to reset anything without a) calling your dad and asking for the old admin password, or b) restarting the computer in an alternate mode of some sort.
However, to expand on what @patrix and @jaberg said, you should not reset (/set) the root password. Resetting the root password is both more difficult and less useful than resetting a regular admin account's password. On OS X, the root account is generally disabled for login because you do not need (or want) to log into it. If you need to do root-like things in the GUI, there may be a padlock to click on & then enter your admin name & password, or you may just be prompted directly. At the command line, you can run commands as root with
sudo (note that it'll prompt for your admin password, not the root password).
You can either change the password to your dad's admin account (in System Preferences -> Users & Groups), or create a new clean admin account for yourself (also System Preferences -> Users & Groups, then click the padlock and authenticate with your dad's admin password, then click "+", choose "Administrator" from the New Account pop-up menu, enter the rest of the account info you want).
You may still run into other leftover password issues, like the Apple ID account & password that was used to buy apps from the App Store; this has nothing to do with local accounts on your computer, so the root/admin/etc passwords are irrelevant here.