I replicated the setup on a pixracer to make sure that the mixer is properly running. By checking the pwm outputs, everything seems to be fine. As you said, the problem could be that the signal to the tail servo need to be reversed. To do so, just change the mixer as follows:
# Tail servo:
S: 0 2 -10000 -10000 0 -10000 10000
However, the thing that still confuses me is when you say:
When I move my channel 1 stick (ROLL) the rudder servo will move. However, when I am moving the channel 4 stick (YAW) the rudder will not move.
Are you sure that the RC calibration is correct? Do you see the correct sliders moving in the Radio tab of QGC?
Also, make sure to bench test the configuration in Acro mode first as reduces the complexity of the control system.