Bringing Children to Synagogue on Rosh haHashanah

Mishnah Berurah to Orach Chayim 587, note 16

"People should not bring their children with them [to the synagogue] because of this reason (to hear the shofar blasts without interruption). It is preferable that [the children] be with their mothers in the women's section of the synagogue, for women are not obligated, strictly speaking, in hearing the shofar. Nevertheless, it is a mitzvah [for a father] to bring [to synagogue] children who have reached the age of chinuch (training), and to keep them with him, and to impress upon them to hear the shofar blasts and not distract the congregation."

Davening (Praying) Out Loud on Rosh haShanah, Chanah and Eli

Hagah to Sheney Luchoth haBerith, Masecheth Rosh haShanah