Can father in law greet his daughter in law by hugging?
There is eternal prohibition of marriage between father and daughter in-law. They are mahram to each other. The following verse sets the rules on covering of women near their mahrams:
“Tell the believing women to reduce some of their looks, and guard their private parts. Tell them not to uncover their beauty except what is naturally seen. Tell them to put their headscarves onto their chests and not display their beautiful parts except to their husbands, their fathers, their husbands’ fathers, their sons, their husbands’ sons, their brothers, their brothers’ sons, their sisters’ sons, their women, those in their possession, those male attendants that have no sexual desire to women, or children who are not yet aware of the private aspects of women. Tell them not to stamp their feet on the ground for their beautiful parts to be noticed. Believers! Return all together towards Allah, so that you may attain what you hope for.” (An-Noor 24:31)
The scholars of Islam agree that a woman does not have to observe strict rules of covering but rather that she is able to uncover her hair, face, arms, hands, legs from below the knee, and feet near these mahram:
Aflah asked the permission to visit me but I did not allow him. He said, “Do you veil yourself before me although I am your uncle?” `Aisha said, “How is that?” Aflah replied, “You were suckled by my brother’s wife with my brother’s milk.” I asked Allah’s Apostle about it, and he said, “Aflah is right, so permit him to visit you.””
(Sahih-ul-Bukhari, Volume 3, Book 48, Number 812)
The body parts that can be uncovered may also be subject to touch by the mentioned persons. The following information confirms this:
The Messenger of God (pbuh) was kissing (his daughter) Fatima, and saying “I keep smelling the aroma of the Paradise from her” .
Considering that milk-kinship is the same as blood-kinship in the respect of covering rules in Islam:
“While Zainab bin Umm-Salama (ra) was combing her hair, Abdullah b. Zubair would come near her, hold her hair, and tell her ‘turn to me’. Zainab was his milk-sister.” (Abu-Bakr al-Jassas al-Razi, Ahkam al-Quran, Beirut, offset Matbaa al-Amira print, V.III, p.315)
It must be known that the permission of contact applies on condition that none of the sides have any sexual desire for each other. If such desire exists, it would be forbidden to discard the covering or allow the contact.
Regarding these , the father in-law hugging his daughter in-law in order to greet is lawful.