AD8422 LTSpice simulation
The input operating voltage range for the AD8422 is from \$-V_{s} + 1.2\ {\rm V}\$ to \$+V_{s} - 1.2\ {\rm V}\$. Your input voltages are about 50 and 200 mV, which is too low.
Your plot doesn't show the differential input voltage to the in-amp, it just shows the voltage relative to ground of one arm of the input.