On my jeep the identical noise and play were the result of a bad u-joint. Even if you don't have a lot of play I'd suspect that's the problem. When putting it into Reverse or even first you load the driveshaft and it will normally clank as it adjusts to the tension. Blipping the throttle in second gear may not cause the noise since the driveshaft is already loaded.
However, depending on how loud your car is, it may be making the noise and you just can't hear it. Ran into the same issue with the jeep.
Hope this helps ease your mind a bit.
Justin