D'Addario began her career at the Joffrey soon after taking one of her daughters to classes at the school (originally called American Ballet Center), which opened in 1953 in a converted chocolate factory. Robert Joffrey and Gerald Arpino had only recently established the company, which had previously been a touring ensemble.
The Times reports that d'Addario's career with the Joffrey began by chance: she answered a ringing phone one day while waiting to pick up her daughter. She was appointed assistant to Joffrey and Arpino in 1961 and five years later she was named executive director.
While at the school she expanded classes for children, pre-professional studies and a summer intensive training project in four major cities in the United States. She also established ballet classes for deaf children, helped form several junior touring ensembles and coordinated the casting of children's roles in the Joffrey Ballet productions of The Nutcracker and Petrouchka.
In her book Joffrey Ballet: Robert Joffrey and the Making of an American Dance Company, Sasha Anawalt writes that "as Joffrey's fierce but benevolent watchdog, [d'Addario] also sometimes made donations to rescue him and the school from financial trouble. Her generosity extended to Joffrey's students: She contributed toward the electricity bills of many teenage scholarship students and often steered them patiently through the terrors of living in New York."
She continued to direct the school until 2005, when she was succeeded by her daughter Gail d'Addario.