First of all, Catholics have CCD (“Confraternity for Christian Doctrine” a/k/a Religious Education).
Children attend CCD from Kindergarten through 8th grade (or perhaps 10th grade for those dioceses that postpone confirmation to 16 years old).
Children need to learn to participate in Mass. And that from the earliest age. I see plenty of parents who have little problem maintaining order as they train their children. Sadly, they are in the minority, but they do exist.
And, frankly, at a TLM parish that I go to frequently (and would go to more if gasoline wasn’t $4 a gallon

), well behaved children are the norm.
I can only speak for my experience when my daughter was young: she quickly learned that receiving a lightly applied “Vulcan Death Grip” was far less desirable than simply paying attention. And if she didn’t get the message with a lightly applied grip, the grip got firmer. No cheerios. No comic books. She paid attention. Of course, we made sure that she learned the prayers of the Mass from a young age. And we talked about what was going on and discussed the readings and all that, so it wasn’t just a boring 45 minutes - 1 hour that interrupted an otherwise fun-filled weekend.
In my experience, the majority of the ill-behaved children are ones whose parents try to keep them distracted with food, drink, or toys, rather than try to teach them. They get bored with the distractions and demand attention.
There are certain children who would only get more determined if they are given the “Vulcan Death Grip.” They relish the challenge! The parents who have these kinds of children understand what I’m talking about.
Children are children. They have children’s minds and bodies, and that’s the way God made them. Even though Jesus is present at the Mass, most normal children still get bored and frustrated with a liturgy that is, for the most part, designed for older children, teenagers, and adults. Their behavior is not “ill-behavior.” The wiggling, whispering, running around, jerky movements, desire to play with a toy, hunger, thirst, bathroom needs, whining, and sniffling/crying is NOT “ill-behavior” if the child is three or under, or sometimes, older, if the child’s body and/or mind has not matured yet. This is what normal children DO. It’s normal and it shouldn’t be punished with a “Vulcan Death Grip.”
Now if the child in question is much older and has shown himself or herself capable of sitting still during movies, television, video games, etc., then a disciplinary action, perhaps a painful one, IS appropriate. But not for little ones.
There are some children who, at an amazingly young age, are able to control their childish impulses and sit still and quiet during adult activities, and chances are good that this is their natural bent and would happen even if the parents didn’t reinforce this ability.
There are other children who are NOT able to control childish impulses and sit still and quiet, even during children’s activities, let alone a long (to them) adult activity.
BOTH of these kinds of children are GOOD children. The one who cannot control his/her impulses is NOT “ill-behaved”. More importantly, both of these kinds of children should be welcome with filial love at the Holy Mass. They are our brothers and sisters in Christ.
From what I’ve seen of the Latin Mass, there are just as many “lively” children as there at an OF Mass.
And we need to keep in mind that Holy Mother Church, in her wisdom, has made it clear that little ones age 7 and under are NOT obligated to attend Mass. Holy Mother Church truly understands that children are children, and for some children, being forced to sit through an entire Mass only incites rebellion. Again, parents with these children know what I’m talking about. There is no sin if parents choose to “ease” their young children into Mass attendance by bringing them for only a few minutes at first, and gradually increasing the time. I agree that at all stages of their development, they should be TAUGHT what is happening in the Mass so that they understand what is going on and that Jesus is Truly Present.