After reading the suggestions, I was able to work through some options and I found my problem: I was emailing the link to the album (the thing like http://www.flickr.com/photos/*user name*http://www.flickr.com/photos/user name/sets/number/) rather than the guest pass link (something like http://www.flickr.com/gp/*user name*http://www.flickr.com/gp/user name/some characters/).
In any event, the corrected process for me is: 1) I have to set ALL the pics in ALL my Groups to Private (using the Group Batch edit feature). 2) Go to the Group that I want to give access to. 3) Click Share button 4) Click Guest Pass, and Private checkbox 5) Cut and Paste that URL in my email to the viewers. Email recipients will get the link and Flickr will open to only that Group and they will be able to view the pics in that Group indefinitely, or until I choose to "Expire" the Guest Pass via the Guest Pass history option.