Has the Prophet, sallallaahu ‘alayhi wa sallam, been authentically reported to have ordered that the children and the insane should be prevented from entering mosques, and that he forbade raising voices therein?

All perfect praise be to Allaah, The Lord of the worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and messenger.

The Hadeeth that you have referred to is narrated by Ibn Maajah, through a weak chain of narrators as mentioned by Ibn Katheer . Al-Albaani and others consider it weak.

Allaah Knows best.