It is narrated from Sayyiduna al-Fadl bin Abbas (may Allah be pleased with him) that the Prophet (peace and blessings be upon him) ordered the weak ones of Banu Hashim and their children to set off from Muzdalifah while it was still night.
Hadith Referenceالمعجم الكبير للطبراني / باب الفاء / 15786