Is it permissible to avoid a friend disliked by the father, by refraining from meeting her or answering her calls, knowing that the father did not force his daughter to cut ties with her?

Filial piety is among the most emphasized duties. If you can convince your father that your friend had no hand in what happened, then do so. Otherwise, it is obligatory to obey him by avoiding her. You can use indirect speech (Ma'areedh) in that regard.