Doesn't look like anyone has mentioned this yet, so I will. You're going to have a lot of trouble turning this module.
If I understand correctly, both wheels are locked together? When you try to rotate the module while the robot is stationary, one wheel needs to spin one way, and the other needs to spin the opposite, because the center of rotation is between them. And when the robot is moving, and you attempt to rotate the module, one wheel will have to turn faster than the other.
What you need is some sort of differential, so that when turning, the wheels are able to rotate independently, but you can still apply drive power to both.
Here's a great old video that wonderfully explains how differentials work (at least in the context of cars)