I am also having a problem with this machine-Alienware 13 with the bottom taskbar-it is too wide and I cannot get it back to the original size of it as it was not always that wide. I do not know how to adjust the width of the task bar.
Place place the mouse pointer at the top of the taskbar until it turns into a double arrow and hold down the left mouse button and drag it down. You can also try starting the computer and booting into safe mode. Once in safe mode restart the computer. Verify that the taskbar is back to the original size.