Dominic Jennings, 45, was once married to Richards' daughter Dandelion Richards, who is better known by her middle name Angela.
On Monday, two days before he was killed on the railway track at Chichester station, Jennings was arrested in London suburb Bognor Regis for allegedly trying to "look up girls' skirts" in a park there.
Jennings' parents and twin sister asked for privacy when asked for comment on the loss by the Daily Mail.
Angela, 48, is the daughter of Richards and his former girlfriend Anita Pallenberg. She married Jennings in 1998 and separated from him "not on pleasant terms" around 2010.
In a Facebook post, Angela called Jennings' sister one of her "closest friends" and offered her condolences to Jennings' family. She explained that her ex had been on "a downward slope for the last 15 years," due to problems with alcohol and drugs.
"I know his family have desperately tried to help and he hasn't accepted it," she added. "It's a shame it has come to this all over social media but he is not the man you all once knew."
This spring, Angela got engaged to her longtime boyfriend, Graham Whitney, with whom she has two children.
Local police said Jennings' death was not suspicious.
Photo: Getty Images