MOSFET Driver Failure
Quite possibly it's the two feet of wire that is forming an inductor of somewhere between 100nH and a couple of uH depending how your wire is laid across the bench.

With a pulse of 4A and 1uH the stored energy is 8 uJ and if this was dumped into the 4.7 uF capacitor when the load was turned off, the terminal voltage would rise a couple of volts BUT if the capacitor were an electrolytic with maybe an ESR of one ohm you could be starting to see voltages on the line to the chip that destroy it. The TC4421 has 20V as its maximum supply voltage.

Try twisting the power wires together and maybe also try increasing the capacitance. 

Looking at your circuit, you have a 2 ohm load so the peak currents would be 6A and this of course means more voltage on the 4u7 capacitor so that would be more like a 3V glitch on the supply taking it to 15 volts. It's getting close! Each time the voltage gets bigger the current taken by the load gets bigger and maybe there is some point when this spirals out of control?



EDIT


  My first test was with a short across the 100 ohm gate resistor with
  the though that the relatively high gate capacitance might keep the
  driver from switching the MOSFET fast enough. That test ended up
  blowing both the MOSFET and the driver.


The MOSFET in your schematic is rated at 16V gate-source voltage max: -



With the ringing and glitching as I've explained above, this is the likely failure mechanism for the MOSFET - puncturing the gate through to the source will be also pretty fatal for the driver too.