"Domenica la figlia era stata tutto il giorno col padre."
Would "... had been with the father ..." work as well? On hover "stayed" doesn't come up as an option but "be" does, yet they are not accepting "had been". My error or Duo's?
Stare would mean to stay, but it's also used to cover for the missing past participle of essere, so I'd say your translation is fine as well.