UPDATE: Thanks for all the suggestions. After reading them, I was able to work thru some options and I found my problem. (FYI, I didn't include this detail in my original post ... I cut and paste the Group URL into my separate email account - I don't use the email link via Flickr.)

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.
Thanks for all the help. I love this site. Given all the suggestions, I guess the chocolate goes to Bart Arondson. Thanks Bart.