H-bridge acting strange
The LA6585 is designed for use with linear Hall effect sensors which have an output voltage swing of less than 1V. The datasheet doesn't say what voltage range the inputs can handle, but I suspect that they don't like being driven to the supply rails. You could try reducing the voltage swing using three equal value (1k~10k) resistors on each input - one resistor to Vcc, one to GND, and the other going to the MCU output. This will reduce the voltage swing on each input to 1/3 Vcc (centered at 1/2 Vcc).    

If you remove Vcc from the LA6585 but leave everything else connected then it could still be powered through its inputs, perhaps via ESD diodes which are internally connected between the inputs and Vcc. Putting high value resistors in the signal lines will reduce this stray current to a low level, and should prevent the motor from vibrating.