User rights of a super user and the administrator
This is by design. A non-admin user is defined by not being able to use sudo (and the graphical equivalent in the mac windowmanager). You can still enter the admin user and password using sudo -u or the graphical equivalent but short of compromising/modifying the built in controls, that's how the system is designed to work.

The su command doesn't work as you expect since the root user in Mac OS X is disabled by default for security reasons. Sudo has enhanced logging and sudo -s gets you the same shell as su - would when a root user is enabled.

So if you don't want to change to using sudo you can enable root on your mac.