Of course you can power the motor driver logic from the motor power supply. The same holds for the microcontroller (toy manufacturers do it all the time). But unless you employ proper voltage regulation, adequate power supply decoupling and proper grounding techniques, you are guaranteed to have problems.
Fortunately, both power supply decoupling and proper grounding are old, old problems with very well understood solutions. However, to apply the standard solutions properly you must fully understand the source and nature of the power supply noise, and due to its transient nature, you will need an oscilloscope to investigate.
For example, does the motor power supply voltage transiently drop below 5V, or are there voltage spikes large enough to destroy the logic supply regulator?