Sampling circuit for decently high-accuracy ammeter?
Putting sensible-sized caps across a 0.01 ohm resistor won't make much difference. 

Instead add a low-pass filter ( a simple one would be a series resistor of much higher value and parallel capacitor) with an appropriate cutoff frequency, and sample much higher than the cutoff.  

Ideally you want it to attenuate frequency components below half the sampling frequency to below the least significant bit. 

Your circuit as shown will only work if the instrumentation amp gets a high enough supply voltage that 12V is within the common mode range of the amplifier. That range often does not include the positive rail.