First I thought that this scene is from the 1938 movie The Great Adventures of Wild Bill Hickok (rating 5), but this is from the 1951 series Adventures of Wild Bill Hickok (rating 7) episode s3e12 (1952).
Not sure about the name of his boy. Probably 12 or 13 yo Robert aka Bobby Hyatt (I think in jeans). He also starred in 3 more episodes.
Rating at least 6-7 for him.
He played in many movies including The Adventured of Huckleberry Finn (1955 Climax! series) as Tom Sawyer, Gypsy Colt and The Roy Rogers Show.