HazardsMind:
If your not sure if the voltage is dropping or not, use a volt meter to confirm that. However, you did say that you put the video monitor on a different power supply and it did nothing, SO maybe voltage drop is not the problem. You are most likely having a shielding issue. Do like G_Mike says, and rewire it correctly.If you want another way to test the RF from the motor, is to simply use an AM radio. Set the radio to a clear station, and try to turn the motor on and off. If you get interference when the motor is on, then you need to shield the motor. My guess is the motors metal casing is not shielded. What you can try is run the motor with the radio on, then use a wire to touch the metal casing to ground. If the interference goes away then you know you have a shielding issue.
My multimeter is digital and it doesn't react anywhere near fast enough to tell me if the voltage drops 
The motor just turns for half a second since it is just a power door lock actuator. It just extends or contracts an arm. Will that be long enough of a duration to try the AM radio test? Also, the same brief interference problem was experienced just by applying a charged capacitor to the circuit.