At those current levels, you can certainly try the motor driver. In the long run, it would be more simple to replace the relays with a logic level mosfet or npn transistor.
Would the diode work that you was talking about? And if so, did you see any on that website that I linked? Its a shop near to me.
Is a rectifier the same thing?
does the rated voltage of the diode need to be above 250mA?
Do they run in line or across the terminals?