I'm sorry; I thought that my description and circuit diagram was enough and the software is trivial and not part of my question; I know how to do the code. The Rapidstrike is a toy foam dart blaster from Hasbro that uses a pair of counter-rotating flywheels to fire darts. It also has a third motor that drives as linear gear system to push darts into the flywheels automatically. It looks something like this:
As I said in my OP; I have modified the wiring as per the given circuit diagram given and want to use an Arduino to PWM a MOSFET to control the pusher motor to fire at a controllable rate of fire in automatic and burst fire. This would mean that S2_Trigger_Switch would instead be connected to the Arduino, and its switching functionality replaced by a MOSFET. The only thing I want to know is how to use a MOSFET in a circuit and still be able to motor brake as it is essential for stopping the pusher motor. Every guide on MOSFETs I have seen has a diode that seems to prevent motor braking to protect the MOSFET.