What is the ruling on the prayer of a mother who is unable to achieve khushu’ (devotional humility) in it due to her child crying and screaming during the prayer, and is it permissible for her to delay the prayer until a suitable environment for it becomes available?

There is no harm in carrying a child or holding their hand during prayer, as the Prophet, peace and blessings be upon him, carried Umamah bint Abi al-As during his prayer. As for smiling during prayer, it is disliked if done intentionally and if it does not reach the extent of laughter.

Delaying prayer beyond its prescribed time is not permissible except for a valid excuse. If it is possible to perform it within its time while carrying the girl, occupying her, or putting her to sleep, then delaying it is not permissible. However, if the worshipper is unable to perform it at the designated time despite attempts, then that is considered an excuse that removes the sin. The blameworthy delay is taking the prayer out of its chosen time, not performing it at the very end of the chosen time.