"You are my third daughter."
Translation:Jesteś moją trzecią córką.
There is nothing wrong with your answer, through usually native speakers would drop the pronoun here, since it is obvious from the verb form. Still, it should be accepted, I think, so please report it next time.
I started without the pronoun, but then it occurred to me that (from my personal perception) relatives seem to use pronouns more often when speaking to each other, even when they are not necessary for clarity. Is that just my family? Anyway, Duo marked it wrong, so I've reported it.
Such things may be a matter of personal preference, but generally the pronoun is totally redundant here. It's not wrong, though. Added now.
Also, it may work very well if you imagine speaking to your three daughters. You look at the oldest one and say "Ty jesteś moją pierwszą córką". You look at the second one and say the same, with 'drugą'. And same thing with the third one. As you actually change the subject while speaking, showing it makes more sense.