Breadboard and 2A.....definetely the breadboard.....ditch the breadboard on the high amp circuit and solder together.
Thank’s for posting it is informative.
Yes the use of breadboard for high current. Is not going to help your cause. Also the wiring layout is also not helping the reliability of the system. If you look at the way the power is wired, it comes from the power supply, then to the FET circuit, and then on to the Arduino. This is the exact opposite of what you need. It should be the other way round, power supply, Arduino, FET.
In fact ideally you should have star wiring on both the positive and negative wires. That means that all the ground wires come together at the same point. The same goes for the supply wires.
Look at this to see what effect chaining as it is called, causes voltage fluctuations further down the chain.
http://www.thebox.myzen.co.uk/Tutorial/De-coupling.html
12V (measured with my multimeter)