Second version of a spot light similar to iGuzzini MK99, modelled from reference photos. The old one is Spot light. The lamp is now rigged to follow a target. On the parent empty there are custom properties to switch the colour of the metal parts from black to white, and to switch the lamp on or off. You can point the lamp to a specific point using the 'target' empty. The rig is pretty rudimentary, but it mostly works. The cable follows the movements of the lamp body. The modifiers are not applied, for easy editing. The model is mid-detailed, avoid close-ups.
Without looking at the file I cannot say more. I have no idea why this is happening. I suggest you try on the forums (e.g. blenderartists.org) and upload the file there.
Can you be more specific? The 'other collections' you mention are instances of this same model or are different objects?
When I append the lamp to a scene and move some of the parts it moves other objects in other collections around too, why?