What is the ruling on going to the accommodation in Al-Aziziyah after departing from Arafat to feed a small child, change her diaper, and fulfill one's needs, then going to Muzdalifah? And how long is the permissible duration after which one may depart from Muzdalifah?

It is permissible for a person to depart from 'Arafat to Muzdalifah after fulfilling some needs in Mecca, if their arrival at Muzdalifah is after midnight, because staying in Muzdalifah is achieved even for an hour after midnight according to the Shafi'is and Hanbalis. However, it is better for a person to follow the Sunnah of the Prophet, peace and blessings be upon him, by departing from 'Arafat to Muzdalifah directly, because going to Mecca first might result in an inability to return to Muzdalifah due to crowd congestion or traffic regulations, and because the aforementioned needs can be fulfilled in Muzdalifah.