Clicking the trackpad button with two fingers on the trackpad is the "two-finger-right(context)-click". That's when you get the contextual menu. You don't have to press the trackpad button to do the two-finger-scrolling. Just move two fingers on the trackpad.
If you don't want to use the two-finger-right-click you can turn that off in the System Preferences and do the conventional control-click to get the context menu.