If I remember correctly, a very big if, all locally mounted volumes were subject to being indexed by Spotlight-even those from a different computer (as long as it was on the local net).

And so to the question….

My wife’s computer is on my local net. We share files etc., all without incident.

But I do not want my Spotlight to index her volume, ergo I have attempted to add her volume to my Spotlight/Privacy pane. But when I do, I always get this response: “This item couldn’t be added or removed because of an unknown error”.

Is there a fix for this or do I just remember all this incorrectly?

According to the X Labs' Spotlight tips, "network-attached or shared volumes are not indexed when mounted." I'm unable to confirm this experimentally, currrently having no network volumes available, but you might try using Activity Monitor to check for indexing activity when your wife's computer is mounted (first ensuring, obviously, that no indexing of your own volume(s) is taking place).

The linked article describes the processes to look for when making this check.

Couple of tips:

1. putting an empty file named .metadata_never_index at the root level of a volume will prevent indexing of that entire volume. (deleting its current index is a separate task, covered by dkmarsh's link). Currently, the only way i know to create such a (dot) file is with Terminal:
   
   touch /Volumes/"your disk's name goes here"/.metadata_never_index
   
   
   
2. We can also shield [the contents of] individual folders from Spotlight's view, by adding a .noindex extension to the folder's name.

-HI-

Many thanks to you both.

FWIW, the X Lab article was just about right for my level of (in)competence. A great reference-now bookmarked.