A question about an instrumentation amplifier and common mode currents
Here's the problem as I see it: -




Irrespective of the InAmp being present, if
electromagnetic interference hit both signal conductors equally, a
higher interfering voltage will be present on the upper wire because
it has a bigger impedance due to Rs. This scheme only works when
there is the same (balanced) impedance in both signal wires.
Linking remote grounds is (usually) bad because any earth fault
currents can flow down the cable and pose a problem for the cable
integrity AND induce voltages in the two signal cables that may add
to the common mode problem and make the InAmp unable to deal with the
common mode voltage all the time.
Both the presense of Rs (unbalanced) and the ground link make
earth currents flowing in the remote ground connection induce an
asymmetrical interference onto the two signal wires feeding the InAmp.