Must a girl cover her face despite her father's strong opposition, which may lead to family problems and a setback for the girl?

Congratulations on your repentance. Fear of hypocrisy is a sign of faith. The conditions for repentance are: abstaining from the sin, regretting it, and resolving not to return to it.

Regarding your father's insistence on you not covering your face, the preponderant opinion is that it is obligatory to cover it. You are advised to deal with your father kindly, advise him with good words, be patient with him, treat him with excellence, and pray for his guidance.