Today's Piano Puzzler

This week's contestants are Peter and Mary-Bess Staffel from Bethany, West Virginia.  This is an oddity:  although I got both parts, it was touch-and-go that I would.  I could tell the composer of the hidden song right away, but it took me a short while to "sing through" the song to get the title, but I did get it.  It's well known, but might not be so for everyone.  And the composer style was very guessable...but...it came down to two possibilities who overlap a bit.  But I guessed right.