Strange oscillation when drving motor with PMOS
I agree that that the oscillations are probably due to the commutator in the motor.

You could try equal value capacitors across R9 and R11 to filter the higher frequencies.

To represent zero current you will need a negative power supply to the MCP6022. This may also be causing it to saturate during the FET off time as the feedback loop will go open, it may take a significant time to come out of saturation.

What tolerance do you have for the 13K and 2.7K resistors? They need to be precision parts to get a reasonable common mode rejection.

Why not put the sense resistor in the grounded end of the motor - you would then be able to sense the current during the FET off time as well to get a motor average current - is this because it is added to an existing machine?

Also you are going over the max VGS for the MOSFET - it is only rated to +/- 20V or it might breakdown.