Instrumentation amplifier - schematic review
AC coupling would make your current reading frequency related. The transformer has to have somehow a reference potential, i.e not floating. If you have a single supply, then it should be biased to Vref/2.







simulate this circuit &ndash; Schematic created using CircuitLab

As said, best way is to have DC coupled signal with anti-alias filter. You will have a DC offset, that you can eliminate it with high sampling and HF pass digital filter (for example > 20 Hz pass). In such way you have all harmonics with true amplitude, no need to re calibrate for 50/60Hz.