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Children with husband Laurence Luckinbill are sons Simon and Joseph "Joe" (who are two years apart) and daughter Katharine "Kate" (who is one year younger than Joe). Sister of Desi Arnaz Jr. Arnaz's efforts to preserve her family's history led to her helping create a genealogy software package, to help others learn how to digitize important data and documents. First choice for the role of Rizzo in Grease, she was allegedly dropped from consideration when her mother, Lucille Ball, called Paramount and said, "I used to own that studio; my daughter's not doing a screen test!" Ball actually owned the studio which was bought by Paramount, Desilu. The part went to Stockard Channing when the casting director remembered seeing her with Arnaz in the 'fifties-themed play' "Vanities." On KGO Radio, in San Francisco (Thursday, Dec. 10, 2009), Ms. Arnez denied this to be the case, saying that she was offered the role of Rizzo in "Grease," but that a lack of solid confirmation, coupled with a conflicting contract, were the deciding factors in her not playing the role. She said that her mother had no participation, aside from counseling her that *she* had to decide between the two offers. Step-mother of Nicholas Luckinbill and Ben Luckinbill. In an interview on a San Francisco radio station she said that growing up she lived next door to Jack Benny in Beverly Hills. Her mother wanted to name her after her cousin Suzan Ball, but her father wanted her to have her mother's name as an honor to her. When Ball drifted off to sleep, Arnaz wrote the name "Lucie" on her birth certificate. He chose to spell her name differently to distinguish mother and daughter apart from one another.