Desi Arnaz reached sobriety toward the end of his life, a proud and emotional moment for his children.

In this week's issue of PEOPLE, Arnaz and Lucille Ball's daughter Lucie Arnaz, 70, reflects on her famous parents' relationship ups and downs, including how his drinking sometimes got in the way. Lucie, who appears in the new documentary Lucy and Desi, says Arnaz got sober with the help of her younger brother Desi Jr.