Translation:She had arrived with her daughter and her husband.
I think it's the other way around, - they add the possessive only when the most plausible is not the owner.
If somebody is pointing with the finger carrying the hat or arriving with the daughter it is safe to assume the finger, the hat and the daughter belongs to that person, - otherwise it would have been stated.
I am a native speaker and I would understand you're talking about the woman's husband. In fact, if I meant to stress that the man is not the subject's husband I would use a possessive adjective ("con la figlia e SUO marito"), but it's more ambiguous than before; more correct and less confusing is "con la figlia e il marito di lei/il marito di quest'ultima". Hope it helps!
duolingo needs to introduce a "swearing in italian" lesson so I can express my dissatisfaction appropriately. I swear to you, the lady said COLLA. I had to fill in the blanks for "e il" which sounded vaguely like "el" but I very clearly heard "colla" all five times I listened to it. This is so frustrating!