Sometimes we can read about these reunions in old newspapers, like this article published in the Dallas Morning News (Dallas, Texas), 4 July 1941, page 3.
Can you imagine F.D. Davis's surprise when his brother Napier from Indiana knocked on his Texas door after they hadn't seen each other for 32 years? There must have been a lot of catching-up to do as the two brothers "spent a couple of days talking over old times."
Then the kicker to the story—after surprising F.D, Napier set off to visit another long-lost brother, Bill, whom he hadn't seen in 40 years!
This brotherly reunion story spreads over Dallas, Texas; Kokomo, Indiana; and Marked Tree, Arkansas.
Hopefully your search to reunite your family will go a lot quicker than the Davis brothers' did!