Is it permissible to bring children to the mosque for Friday prayers if they might distract the worshippers, and what is the response to those who cite the hadith: "Keep your children and your insane away from the mosques"?

Children in the mosque fall into two categories:

First: Those who do not play mischievously or cause harm; there is no objection to their presence, provided they are taught the etiquette of the mosque.

Second: Those who play mischievously, cause harm, and do not stop. Such a child should not be brought to the mosque, and if brought, should be removed due to causing disturbance.

The hadith: "Keep your mosques away from your children and your insane" is weak and does not absolutely prohibit children.