Integrated H-Bridge (ST VNH3SP30-E) suitable for low-side current-sensing?
You don't say how much current the motor needs, but because it uses Hall effect instead of a shunt resistor this sensor (ACS712) has a very low internal resistance of 1.2 m&Omega;. That's only 12 mV drop at 10 A. Sensitivity up to 185 mV/A.



Notice also that the high current path is galvanically isolated from the signal ground in this sensor.  That can solve the ground offset problem.  IP- may be connected to power ground, while GND can be connected to signal ground.  VIOUT will be referenced to GND.