In English there's no such distinction, but here it should be 'Oni nie uwierzyli swojej córce.' The sentence with 'ich' suggests there are two groups of people, the ones that haven't believed, and the others, her parents.
nie wierzyli swojej córce would this sentence not be more correct
If I understand well, then is the meaning of this sentence : They don't believe the daughter of ( for instance ) their neighbors
Can someone tell me why "trust" instead of "believe" is wrong?
Although related concepts, there are seperate words for each. Trust = za(ufać).
Interesting. In Russian, wierit'/powierit' means "to believe" and dowieriat', "to trust."