Mosfet not passing enough current using a microcontroller and 2 power supply
You may not be driving the mosfet into full saturation.  I see the controller runs from 3.7 volts (4.2V hot off charge).  A little low for proper gate drive voltage.

Try using a gate driver to drive the gate of the mosfet.  I found one on digikey or mouser that not only drives the gate, but does level conversion as well.  You could drive it's input with 3.7 Volts and use the 7.4 Volts to drive the gate. Check out the UCC37322