Does it make sense to use differential ended inputs to measure current signals with shunt resistor?
As drawn in your Figure 1 everything should be fine as the sources are isolated from ground. All three circuits are grounded at only one point.

The original circuit concerns me a little in that there is a different ground present at each end and this implies that a variation in potentials is possible. With one circuit as show this would be the same as introducing a voltage source on the ground / return line but due to the current drive you would still get the correct voltage drop across the shunt resistor. The problem is that with three such circuits and a common ground (as in Figure 1) you're going to get circulating earth currents and it will rapidly get difficult to figure out what's going wrong.

Stick with Figure 1 and isolate your sources, if possible.