Once you have gone a little further down the path and identified potential kids (and you will have an advantage if one child is a girl and married someone with an unusual name) it can be worth sending messages on facebook.
I did it to potential relatives of my grandmother - her maiden name is very unusual - so I looked for people with that surname in the town she was born and sent them a message, basically saying I know it's weird and a long shot but was looking into my family history and grandmother was X and was born in that town but had had no contact with her family since the 1920s (she had a child without being married and I wondered if that was the cause fo the rift), and was wondering if they could help or knew anyone who could, and giving my email.
A cousin eventually found the message and replied, saying he'd never heard of my grandmother but as far as he knew there was only one family in the town with that name - and put me in touch with his uncle who had done research into it, but gave me the name of his grandfather - his grandfather was my grandmothers little brother.
When I then spoke to the uncle he believed that his father's sisters had both died - one did as a child, my grandmother hadn't - but it seems her parents told her brothers she had
Worth trying modern methods too