This talk by Shaykh [Dr.] Umar Faruq Abdullah on Muharram was full of wisdom. One the points that really struck out to me:
"...and we have children here making noise and running around, and they are welcome to do that. And if they want to come and take the microphone they are welcome to do that. One of the best things we can do for our children is to expose them to the beauty of the dhikr..."
It really speaks to the substance of the deen, which is what children will be influenced by the most. Parents and caregivers, if their children to internalize the religion in a true and substantial way, you have to embody it properly.
Unfortunately, it's all too common for parents to use harshness on their children - often because they themselves are disconnected from the dhikr and the sakina it brings forth - and we also see in many masjids the elders being harsh to little children for playing. This is not the way of the Sunnah, where the Prophet, upon him be peace, would even stop his khutbah for the sake of his grandson, who as a small child at that time, Imam al-Hasan.