RFK Jr.’s Family Doesn’t Want Him to Run. Even They May Not Know His Darkest Secrets.

Twenty years ago Robert F. Kennedy Jr. appeared in an HBO documentary about the dangers of a nuclear plant on the Hudson River. Indian Point: Imagining the Unimaginable, directed by his sister Rory Kennedy, pits the crusading Kennedys, pictured flying in a helicopter over the nuclear facility, against Entergy, the power company. The film argued that the surrounding environment would be made uninhabitable if the plant came under terrorist attack.

This was necessarily a high-stakes confrontation. In anticipation, Rory warned her production team they had a potential liability: Her brother, though a prominent...