I wouldn’t trade having children in our meetings for anything, and, as bluntly as I can put this, they aren’t the problem. The adults are, and I say this from the perspective of quite a few years sitting in front of the chapel looking out over the congregation. Here are a few of my observations:
1) Reverence is not quietude. It is an internal feeling of awe, respect, worship - of "revering" something.
2) Children who see their parents or other adults talking in Sacrament Meeting will learn to talk in Sacrament Meeting. Children who see adults not being respectful and worshipful will learn also to model that behavior. This is particularly disheartening during the actual administration of the sacrament, when awe, respect and reverential worship are the heart of the very purpose for the ordinance.
3) Reverence does include a degree of quietude in situations where quietude is appropriate - like the administration of the sacrament. Children who are not taught to be quiet outside of Sacrament Meeting, as a component of reverence, will not be able to be quiet during Sacrament Meeting. I know my wife and have been blessed with children who do not have difficult issues that make being quiet particularly difficult, but we also took time each week when they were pre-nursery age, at home, to sit with them on our laps for extended periods of time (while reading or talking quietly at first and then simply “thinking”) - specifically to help train them to be able to sit silently during the administration of the sacrament and quietly throughout the service. They aren’t perfect little angels, but they don’t distract from the spirit - even when my wife was alone with all six of them.
4) Parents (or mothers alone) who struggle to control the chaos of a disruptive child and others they simply can’t leave alone need others (adults and/or teenagers) who are willing to ask privately if they can help - either by sitting with the family throughout SM or moving to them when the parent(s) needs to leave with a child. The screaming child isn’t the issue; the mother or father not feeling like s/he can leave is - and that is a problem of lack of service within the congregation. The parent who blithely sits and ignores a screaming child also is much more of a problem than the child, and a parent who chastises in again during a time requiring reverence also is a problem.
5) Many husbands and fathers need to take a few slaps upside the head and stop acting like dealing with the kids in Sacrament Meeting is their wives’ job. There is a heavy dose of repentance necessary for many.
There are more examples I could give, but I believe firmly that the issue is not kids in sacrament meeting but rather adults abrogating their responsibilities for those kids. Jesus said, "Suffer the children to come unto me" - and allowing them to worship with us is one way to help fulfill this request, imo. God bless the parent (usually the mother) who sacrifices a bit of her own peace and sanity in an effort to bring her children to Christ and help them learn to worship Him. NOTHING in this post should be used to make that good brother or sister feel guilty when children still are learning reverence and simply being children.
In our ward now, our last Bishop focused a lot of attention on humbly and gently teaching the adults to take responsibility for reverence in the chapel, especially during the administration of the sacrament. The difference in our ward over the past few years has been nothing short of amazing - even with plenty of children in our midst.