"The father cried taking his girl from school."
Translation:Tatăl a plâns luându-și fata de la școală.
It is a reflexive dative pronoun, used in this case to express possession, i.e. that the father takes his girl from school.
I think (someone correct me please if I am wrong!) that the sentence could also take on this form:
Tatăl a plâns luând fata lui de la școală.
Yep, both of the above are correct.
We could've also said:
Tatăl a plâns luându-și fata sa/lui de la școală.
I guess that with "sa/lui" there would be a little more emphasis on "his girl", although the most common/normal form would be the one in the translation (Tatăl a plâns luându-și fata de la școală), but other forms are possible and not extremely rare as well (like those above).
Also, just to clarify, "sa" is a possesive adjective, and "lui" is a personal pronoun, but they kind of mean the same thing, although "sa" sounds a bit more formal, while "lui" is a bit more informal.
Oh, and other thing, as an example, if we would've eliminated the "și" in this sentence, then it would've been "Tatăl a plâns luând fata de la școală.", which means "The father cried taking the girl from school", so we don't know if the girl he took was his or not, thus "și" showing that to us.