Can you be more specific about what you see? Any time you install a new Norton security product it will always remove any previously installed version.
Welcome to the forums. Can you please provide us a screenshot, where you are seeing two instances of NIS ?
Is it in Task Manager or in the System Tray or in the Windows Gadgets ?
Can you please Restart your Computer and Check the Widget and the Icons by the System Tray by the Time and Date.
Nothing to worry about the attack of the clone icons. You can close any one widget and are you still having the clones in the system tray next to the time/Date?