A: A real skeptic, aren’t you? No, if the mouse works fine on another computer, this points you away from the mouse itself as the problem. You’ve done one of the best tests of a component by removing it from its current connection and trying it out on a completely separate device.
Yes, it could (maybe) still be the mouse. and plugging it into the laptop may have been the one extremely lucky chance this one time that everything fixed itself as you were carrying it from one place to the other, but this is not the likeliest diagnosis.