I think you are using a ICL7660 to get the -9V. It is not a good clean supply.
Here I added a RC low pass filter to the POT to remove the 10khz noise that is on the power supply.
View attachment 107553
It is possible that 10khz noise on the -9V can get into the op-amp. Probably not likely. Can be reduced by adding a RC filter.
The LF351 (and its ground) might not be connected well to the micro computer. Add a capacitor from ADC-input to the analog ground at the micro. Add a resistor to make a RC low pass filter. This filter will average the noise out.
AND: Add a 0.1uF cap from +9V to ground and -8.5V to ground on each op-amp.