Changing direction of DC motor
Since you have both a V+ and V- you could just use 2 transitors. If you look at an H-bridge, you only need half the circuit. 

The only problem is that you need V- to disconnect the NPN transistor, and the arduino can only go as low as GND. So you'd need a second transistor to drive it. 

The same might also be needed for the PNP side, if the arduino voltage is regulated to a lower value than V+. 

I found this schematic applicable, but only use the left side. The right side of the motor should be connected to ground (or the middle voltage of your battery). , and replace the opto's with normal transistors.


Come to think of it, I'm not entirely confident about replacing the bottom opto, since battery-negative is below GND in your case. I think it should work, but I'm still quite new to this stuff.

Also make sure you add something like 1k resistors to the base of the transistors (that replace the opto's)