Is it permissible for a girl to wear the niqab despite her father's strong refusal, or is parental approval in this case more deserving?

Obedience to parents is restricted to what is good and permissible, for there is no obedience to a created being in disobedience to the Creator. The niqab is obligatory according to the more preponderant opinion, so it is not permissible to obey parents in removing it unless there is a necessity or a need that is considered equivalent to it. If wearing it results in real harm or injury from the father, then there is no blame in taking the concession of acting upon the less preponderant opinion to ward off harm and out of consideration for her situation.