You should do absolutely nothing.

You do not owe any proof to her dad. Her dad took the position he took because of a combination of prejudice, ignorance, and overly protective attitude towards his daughter.

He is also overly controlling of his daughter because I am sure she did want to say goodbye at least, but he did not let her.

He wronged you, in a way, and in way, wronged his daughter by not allowing her independence and freedom of choice. He dictates her choices.

what would you be proving to such a man?

Whether she needs to do something depends on what she wants. But let her figure it out on her own. Do not contact her dad because it might turn to be deeply, deeply humiliating for you and would reverse, in an instant, all the wonderful progress you have made feeling better