The chapel is sacred and kids are very capable of being reverent. They can be trained that there are places to play and there are places to sit quietly.
Dogs are less developed creations than humans, yet dogs can even be taught to sit and not take food when they are hungry or sit and not chase distractions, even though it is their natural instinct. It takes a long time to teach them to be obedient and the same is true of children, but it can be done if one is diligent.
I heard recently of a primary teacher that was sitting with a child in primary. The child was saying they wanted to go to their mom for food. The teacher told her it was not the time. The mother was in the room and looked to the child and told her to stay there. After several minutes they were winning. Then the child started to cry. The mother immediately gave in and reinforced with the child that if she behaved badly she would be rewarded.
The chapel is heaven. Anywhere else that you have to take them because they are misbehaving is hell. When they throw a fit, swiftly take them out and find a spot where you can make their time outside of the chapel more uncomfortable than their time in the chapel. Often finding a spot where they can throw their fit without disturbing the chapel is useful. I generally use a class room, but if they are especially vocal you can take them out to your vehicle.
Outside of the chapel must be exponentially more boring and painful than inside the chapel. Just letting them sit and play is not painful.
I say take them out swiftly, because this shows that their behavior will not be tolerated for any length of time and if they are noisy enough to get your attention, then there is trouble coming. Eventually because they know the trip to the hall is immediate and painful, many times just a stern look is enough to put their seat back in the pew and to button their lips.
Turning the pew into a playground can also disturb those around you even if the kid isn't screaming. You may tune them out, because you have giving them something to play with and they aren't screaming. While at the same time, no one around you can focus because the kid it scraping their toys along to back and side of the pew or is staring at the people behind you or are kicking the pew or are grabbing the people in front of you.
The chapel is sacred. It is not a playground.
When to Start
I'm not sure that any age is too young to start training. Obviously you must tailor it to each child, but even babies can be taken to a plain room to be quieted, rather than the hall. You can hold them and rock them, facing a dull wall in a quiet place, which will make the chapel seem entertaining with things going on their.
Missing Spiritual Instruction
Some may think that they will miss out on the lessons and talks by taking their kids out of the chapel and out of the hallway where the parents can hear. You will miss less by taking a few weeks to train the child. Besides that, training the child is your top priority. In reality, how much are you getting out of the meeting out in the hall with noisy kids and chatty parents? Once your kids sit quietly you will get more from the meeting and you can leave the chatty parents in the hall.
As you have more children the process will be helped along as they learn by example of the others.
Teaching Them Reverence for Sacred Things
If they learn reverence for the chapel, they will learn reverence for other things in life and respect for people that are speaking to them.
Just like Sunday is different than other days, the chapel is different than other rooms. There are things we don't do on Sunday that we do on other days. There are things we don't do in the chapel, like play and eat, that we do in other rooms.
Just like we dress differently on the sabbath, we all dress different in the chapel.
The chapel is one step closer to the temple than any other room in the church meeting house and it should be treated as such.