Is the prayer considered valid when attempting to alert another child during prayer about a small child's actions, and is it better to delay the prayer to avoid this and focus better?

There is no harm in a woman clapping to alert a child, because clapping is permissible for her if something happens to her during her prayer. Similarly, raising her voice with the Qur'an or dhikr to alert someone does not affect the validity of her prayer. Likewise, there is no objection to delaying prayer from its very beginning or middle to perform it with tranquility and humility, as long as its time remains.