AD8221 for high side small current measurement
The AD8221 is specified to work with a maximum supply of plus and minus 18 volts. You have applied plus and minus 30 volts. Yes I know it’s a simulator but why should the model be expected to perform sensibly at levels way beyond what the real chip is designed to operate at.

Also, I see that your driver rails might create much bigger voltages than what the common mode input range of the AD8221 can reliably cope with.

Maybe also, the problem is the overshoot and ringing because on the lower current sensing leg, opamp input capacitance will somewhat quench that ringing and, because the AD8221 is operating differential, it will over-amplify the ringing artefacts when the voltage changes.