Sorry Paul... my Lysdexia is playing up again and I mis-heard your last post...
Yes you can swap the external HDD from PC to lappy. You'll just need to install Second Copy on both, set up appropriate profiles in each, and have separate destination directory on the external HDD for each.
E.g. I have directories set up:
K:\Dcopy
K:\Lcopy
K:\NotebookCopy
Not sure what'll happen if you don't have the HDD attached when an auto profile runs??? If it's well written software it should give you an error message and that's all. I would probably tend to make the PC auto profiles and the lappy manual? It's up to you. Think about it though.
Al.