What is the criterion for defining prophetic characteristics, and is it permissible to use the action of Al-Hasan and Al-Hussein during the Prophet's prayer (peace be upon him) as evidence to justify children playing during prayer?

The unique characteristics of the Prophet, peace and blessings be upon him, are not established except by authentic proof, and many authors have been lenient in mentioning them. It is permissible to bring children to the mosque on condition that they do not play idly in it, or that they stop if they are told to; this is to keep the mosques free from idle talk and play. As for what the Prophet, peace and blessings be upon him, did with Al-Hasan and Al-Husayn during prayer, it was not a matter of play, nor was there any special privilege for them in it. Rather, it falls under the permissibility of carrying children during prayer and performing minor actions within it out of necessity.