This is, "Dear Old Dad," from a very little-known musical that played off-Broadway in 1961. It has an important footnote in Broadway history, though, being the first book-musical with lyrics by Sheldon Harnick. However, the music was not by his longtime partner Jerry Bock, but a fellow named David Baker. Adding to this oddity is that it has an odd timeline. It was performed off-Broadway after two Harnick-Bock shows, including the Pulitzer Prize and Tony-winning Fiorello! However, it had been written before both, and initially performed in Dallas.
The show is basically a satire on the Horatio Alger-type stories. And this song, sung by son and mother to the memory of "Dear Old Dad," fits right in with that in it's very tongue-in-check whimsy.