The difference you are seeing at idle and while moving is probably due to the voltage difference. When a car is idling, the alternator doesn't produce the same output as it does when above 1500 RPM. Since you say it has a choppy movement, your cable is probably bad. When it is moving slow, the cable is causing drag and with the lower voltage from the charging system, the motor doesn't have the power to move it. This is just a guess though.