The problem is with the ladder rung that enables the TIMER, StopButtonDelay.
You must press Emergency_Butt for a time period that is longer that the time period of the StopButtonDelay TIMER or the output of the TIMER will not go TRUE.
I think that you need to take a step back and a deep breath. Your code is a lot significantly more complex than what you described.
I think that you can get most of what you want with 2 lines of ladder logic and one RELAY.
In this example the first ladder rung is a typical, PLC style, latch. The RELAY, Stop_Button, is latched when the Emergency_Butt is pressed. The RELAY is cleared when the TIMER, StopButtonDelay, expires.
The 2nd rung controls the TIMER, StopButtonDelay. I added the NC version of Emergency_Butt to not allow the TIMER to run until the StopButtonDelay is released.
Best of luck,
Gary D.