The best solution that I can think of is to hook up the desired external drive(s) to computer 2, copy the catalog file from computer 1 to computer 2, and work on computer 2. When you are done, you would have to copy the catalog file back to computer 1 (and replace the existing catalog file).
OK, so I do need access to the originals on computer 2 (laptop)? It's true that I cannot accomplish this with a catalog on computer 2 that has the previews only, while leaving the hard drive connected to computer 1? I'm trying not to move the hard drive as it's being used by another person. But If I need to I may have a workaround....
Thank you for your fast reply!
So you want a more difficult solution where the hard drive doesn't move.
On Computer 1, create Smart Previews for the desired photos. Then transfer the catalog and smart previews to computer 2. The catalog on computer 2 does not need the photos if the smart previews are present. Do your work on computer 2, when done copy the catalog file back to computer 1. All of this assumes that no work is being done in the catalog on computer 1 while you are working on it using computer 2.
Exporting and importing catalogs will get you where you want to go.
When exporting the partial catalog to the laptop, pay attention to the options for handling the original image files. You may need to copy the image files, at least temporarily, for the smart previews to be generated.
Since the desktop catalog already has the image files with it, importing the edits from the laptop will not need to bring the image files back over.
This is exactly what I was looking for. Thank you so much!!! Awesome response!