Thanks for posting! Definitely strange behavior you describe and I’ll be happy to help.
Thanks for your description of the issue as well as taking the time to do some troubleshooting. Our dock does not have any controls over keyboard input, so I would not expect it to cause this behavior but it is not out of the realm of possibility.
You mention that unplugging all peripherals from your dock (leaving just the power adapter connected and the USB cable to your system connected) at work still propagates the phenomenon. Based on this fact can you test by physically swapping your two docking stations?
If possible, can you take your dock from work (I will call this Dock #1 for simplicity sake) and test connecting to it at home using the different USB cable while all peripherals are disconnected and then take your dock from home (Dock #2) to work and test connecting using the different USB cable while all peripherals are disconnected? This will both test the docks themselves as well as the USB cables (which could be a potential culprit) to see if the issue ‘follows’ the dock or not. If Dock #1 behaves in the same manner at home, using the known good USB cable from Dock #2, then we may have isolated the issue to just the hardware of the dock. If using Dock #2 at work enters a random key and shows the same behavior while using the USB cable from Dock #1, then it could be the USB cable that is causing the issue.
Please let us know the results of physically swapping docks and we will go from there.