But can you see what C1603 is doing?
It decreases closed loop differential gain of U1601B, which means that U1601C is mislead to believe that transmitted AC current is lower than in reality. If you remove the filter and test with 10kHz signal, you would likely find that the regulator transmits more current than at 10Hz, for the same input amplitude.
Furthermore, it ruins AC common mode rejection. Common mode signal present at the positive end of R1613 is simply passed to the output of U1601B at unity gain, due to direct feedback through C1603. This causes all sorts of extra oddities, dependent on load reactance.
The whole thing looks like its exact behavior is needlessly difficult to predict. But no, I don't have any sim example where it clearly oscillates. The phase dip I have shown is not -90°.
I don't think there would be much wrong with:
- removing C1603, to make U1601B work as proper differential amplifier, giving accurate (amplified) image of R1613 current, up to tens of kHz that this chip ought to be capable of
- increasing C1602 to a few nF (or more) to dumb down U1601C a little more; above a few kHz it will simply be a voltage follower, ignoring any feedback coming from U1601B