All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
It is religiously permissible for a daughter to hug her father if there is no suspicion and if she does not fear any temptation. However, if this raises suspicion or that she fears temptation, then in this case, it becomes forbidden. Abu Daawood reported that Abu Bakr kissed his daughter ‘Aa’ishah on her cheek. Moreover, Ibn ‘Abbaas said: “The Prophet hugged one of his daughters who was breathing her last, and he put her (head) on his chest and she died while he was holding her closely against his chest.” [Ahmad, Ibn Hibbaan and At-Tirmithi] Shaykh Al-Albaani classified this Hadeeth as Saheeh (authentic).
Therefore, this should not be done in public as this contradicts being modest which is a good trait. ‘Imraan Ibn Husayn narrated that the Prophet said: “Modesty does not bring anything except good.” [Muslim]
Hence, your female friend is wrong by doing so in public especially that doing so in public makes people suspect her and her father and doubt about them, whereas avoiding suspicion is something that is religiously required. Therefore, she must avoid doing so in the future.
In any case, this conduct does not affect the marital relationship between her father and mother at all, neither according to the Hanafi School of jurisprudence nor according to any other School of jurisprudence.
Allaah Knows best.