Electronic – Grounding problems

Trying to send these kinds of signals 30 feet all together on the same cable is nuts. A much better overall architecture is to send power and simple digital serial signals over the cable. Handle the details of the stepper control and sensor readings at the far end of the cable, and receive commands and send results digitally. With the CAT5 cable you described, you can use one pair for transmit, one pair for receive, and the remaining two pairs for power.

Russell has described some things you can do to try and make this mess limp along. Maybe if you're careful those are good enough. However, the real problem is in the higher level architecture, which is where any real fix will have to be made.

Do you have a de-coupling capacitor on the motor itself? If not, add a 100 nF ceramic capacitor across the motor terminals, as closely as possible to the actual motor housing. (Worst case, across the connectors to the motor terminals on your board.)

Does the motor run only one way? If so, also add a dissipation diode across the motor, with anode towards ground.

To get a better measurement of the voltage across the sensor, you may be able to use Kelvin-style wiring (or "remote voltage sense" wiring) where the actual sensor wires are separate from the current carrying wires. Whether this works depends on how the ground for your 1.5V reference is created.

A separate battery for the motor only seems like a good idea. If you can't do that, at least put a voltage regulator between the 3.7V battery and the rest of the circuitry, regulating down to 3.3V or so. (You'll need an ultra-low-drop-out regulator, such as a LF33AB or better, to do this.) Regulators typically damp 80 dB or more of noise. Especially if you keep the grounds separate.