[Dr. Sivana]

I'm guessing old Francis Ford Coppola got advised not to include this in the movie version.

Coppolla filmed something VERY close to this, a child star at Woltz' having a birthday party and getting a pony. What happens is more than a little implied.

The scene never made the movie, which was already running long.

https://www.youtube.com/watch?v=Lkp9UnXM72Q

[Dr. Sivana]

Second part:
https://www.youtube.com/watch?v=13EmjpXQ8_w

[Steely Tom]

Wow, I never heard of that. I had no idea those scenes had ever been shot. Amazing.

I do remember that (in the book) Tom Hagen tells Vito Corleone about the little girl, all the details, and the Godfather shakes his head and says "infamita", a word which he uses to describe drug trafficking later in the story.