I learned an important lesson. Go back and try again. I found from another search of "The Day" which is an old New London, CT newspaper, a very small article but with answers to a couple of important questions I had. Were they married? I had never found any documents confirming it. Well, this little article was about my Grandma suing Grandpa for desertion and requesting custody of their two daughters Leona and Nellie. It listed the date of their marriage (yay). Turns out Grandpa was kind of a rat. He left Grandma in Connecticut and went back to what must have been his much-missed South. Of course, it seems impossible to get all the facts at this point. But I was happy to learn this part of the story and now I can try to get a copy of their marriage certificate. I also need to get his death certificate to verify the information I have, but from knowing nothing to knowing even more than my mother probably knew about her paternal side, I have filled in almost all the blanks.
So if you did a search once - go back and try again - you might be rewarded with some answers.