Noise in op amp design or EMI?
It's oscillating under load conditions because the 100 ohm resistor feeding the gate forms a low pass filter with the gate-source capacitance (well about 50% of it) and adds another few tens of degrees of phase shift and, at some high-ish frequency the phase margin is no longer a margin and it oscillates.

Two things make it worse: -


The 100 ohm resistor (as mentioned above)
The buffer op-amp from the sense resistors in the feedback loop.


You could try getting rid of that buffer op-amp and replacing it with a series resistor from sense resistors to the inverting input of the main-op. Then add 10nF feedback capacitance between inverting input and output of said filter. 

Or, you could just bypass that unneeded op-amp and see what happens AND reduce the 100 ohm resistor.