"That computer" , it does not happen on others regularly, and it likely is not the mouse when other mices do the same thing on the same computer. This makes it more likely that it is dueling softwares.
More than one input device softwares can hook into the mouse control, could be you have 2 softwares running that are hooked in, that includes trackpads,touchpad software also. Does it do it in safe modes?
Because you have applied more than one mouse item on that computer, you may have also installed more software than one mouse needed. Because the mouse control software for windows links the port data into the system, much the same way as any other input device software, it would be easy for the software to remain operational, even when that particular input device is no longer present.
The simplest first thing to do would be to look in your Programs and Features listings in the control pannel, and see if there is software that you can uninstall, because it is no longer needed. With all 3rd party input device software removed, generally there will still be the MS default driver items left, compatable with most simple mices, and the simplest operations will still function.
other notes: While the optical sencor and comparitor routines (used for the wheel) could be prone to reversal when dirty or flawed circuitry, it is unlikely to happen in all your mices at once, and likely to bounce around during any single movement of it, not reverse for the whole move.
There are input devices that have full hardware ID, and the software for those devices will not be functioning without the device present. Depends on the complexity of the device and software, and methods used for programming. Much of the simple software though is more cross compatable between them, and could create a conflict.