DulcimerJones (or can I just call you "Jonesie"?),
It holds a lot of memories for me, too. My mom used to sing it to me when I was but a little shaver. I forgot about it completely until recently when I started playing it again with a ragtime pianist of my acquaintance. He plays the original 3-part tune "Iola" from 1904.
Then in 1940, a fella named Saxie Dowell stole the middle part for his song, "Playmates". Johnson sued over the plagarism and won. However, at the time "Playmates" became popular. Kay Kyser had a hit with it with Sully Mason and His Playmates on vocals, as did a few other people.
In 1955, Which is probably the version that you and I are familiar with, the record was a hit for The Fontane Sisters.
Even more recently, it was used in The Addams Family movie with vocals by The Kipper Kids.
And there you have more than you ever needed to know about "Iola: A Ragtime Intermezzo".