Uno - measure the voltage, NOT connecting GND
If I understand the description correctly, neither side of the resistor is at ground potential.  There's a wide gamut of methods of dealing with this, for example using a differential ADC unit, or using an instrumentation amplifier ahead of a single-ended ADC.  But perhaps the simplest method is to use two ADC channels, one attached to each end of the resistor, with ADC ground connected to some common reference point.  Measure both voltages and take their difference .