I know when my brother got divorced several years ago--in a different county--it had to be published in the newspaper. When Grandma passed, and we were going through stuff, we found the little book that was handed out at his first wedding, with all the pics Grandma had kept, and the clipping from the newspaper that showed their D was final. Was I glad his new wife didn't find it!!!
I'd test it out like Tearsoflove suggested so you know what to expect.
If you're concerned with what your children may find out in the far future, watch what is published with the obits in your area--morbid, I know. I googled my deceased-for-many-years-grandfather and found out that he had another child in a different state that no one in the family knew about and I have a half-first cousin that knew there was another child but knew nothing about the rest of us. All the players in this drama--grandfather's first wife, both of the children, etc. are now deceased, but it was a shake up to everyone to find out this stuff many, many years later. Hope this isn't a t/j, but family information hangs around forever.