I think the idea of cr0sh would work as outlined. The PWM transistor will switch the relay ground connections and the existing transisitor will determine which motor terminal gets connected to ground/power.
This would also work as an Arduino controlled on/off switch which is missing from the current design. An H-bridge would obvoisuly be preferred if fast direction switching is needed (as the mechanical relay will wear), but for many applications it may be suifficient (e.g. manually operated doors).