It doesn't appear to DRAG the line anywhere, but once you get it to where you want and release, it will work. I re-created the circumstances you described exactly. I saw the quick launch shortcut move to the right when I turned it back on. It's easily moved back to the left my clicking on the line, holding it and then dropping it back on the far left line.
Just reloaded the system after hack of the registry and removal of powertools (I'll put powertools back on for a couple of its features.)
Now it works as it is supposed to. Don't know if it was powertools or my removal of prior desktop from the registry - but the system is up with no reload of all software, and quick-launch can be swapped left or right with ease. Used Norton System Works to fix a couple of minor DirectX problems always present after reloads, and now have 100% system.
Restoration of prior desktop settings will be easy now, and my friend can come pick this puppy up! Thanks again.