Correct me if I'm wrong, but if you reverse the polarity at the motor, won't it spin in the opposite direction? That is, if the motor runs clockwise while positive is connected to positive and negative is connected to negative, won't it run "anticlockwise" while negative is connected to positive and positive is connected to negative?
If that's the case, then a set of relays should be enough to make it run forwards and backwards. However, as mentioned before, you don't just want to slam the motor in reverse while it is going forward at full speed. You may need to add a timer to the circuit to give the drill time to slow or stop before changing it's direction.