Isn't it ironic that Catholics are (rightly) renowned for being pro-life, yet many parishes are less-than-welcoming of families with young children unless those children are robots? Isn't it ironic that many parishes have statues of/devotions to the Holy Family and/or the Infant of Prague, yet don't welcome the babies and toddlers in the pews? And then, when these families find it too stressful to continue attending Mass or bringing their children to Mass, everyone complains that people are leaving, the parish is dying, and vocations are decreasing. That should hardly be surprising, though. Those who remain despite the sometimes-daily looks and comments end up being stressed at times. At least I do. The children also sense it and can dread going to Mass, which is not good at all.
While not an exact parallel, I cannot help thinking of this passage from James 2:1-5 (New Jerusalem Bible):
"1 My brothers, do not let class distinction enter into your faith in Jesus Christ, our glorified Lord.
2 Now suppose a man comes into your synagogue, well-dressed and with a gold ring on, and at the same time a poor man comes in, in shabby clothes,
3 and you take notice of the well-dressed man, and say, 'Come this way to the best seats'; then you tell the poor man, 'Stand over there' or 'You can sit on the floor by my foot-rest.'
4 In making this distinction among yourselves have you not used a corrupt standard?
5 Listen, my dear brothers: it was those who were poor according to the world that God chose, to be rich in faith and to be the heirs to the kingdom which he promised to those who love him."
When it comes to families with young children, the distinction isn't between rich and poor, but one of outward behaviour. If your children can be perfectly still and quiet, you are welcome to sit in the front, but if they cannot, you are told to sit or stand to the side or back. Thus sitting where the children can actually see becomes okay only if those children are not audible or visible, in some people's opinions. (Note: I don't ascribe evil intent to any such person, and so I harbour no ill will. I blame societal views, personally).
Mixed in with all this is the idea that a "good" child is one that is not seen or heard - in other words, one who doesn't act like a child. Yet Jesus was a child, and He surely cried and played like any other child, since He is like us in all things but sin. And babies and young children are incapable of committing personal sin. That's not to say that parents don't or shouldn't direct their children, but that children crying, talking, and moving is normal and not bad. And the child's parents also aren't bad parents. Can they be distracting? Yes, but so can lots of things. I've been distracted by cell phones and the lingering smell of cigarette smoke, but that's my problem. I'd never suggest such people move for my benefit, because it isn't about me - it's about our Eucharistic Lord!
All this sometimes makes me wish I were Byzantine Catholic. I've been told that in the Byzantine Divine Liturgy, children move around and look at the icons. This is expected and encouraged, because they are then being taught about their faith. Unfortunately walking around looking at the stations of the cross and statues isn't usually encouraged in Latin parishes, though I do point them out during Mass at times.
I suppose what I'm getting at is that we can't just welcome certain people. We can't restrict our welcome based on appearance, age, etc. We must live the Gospel. I'm far from perfect at this, believe me. But also believe me that I know firsthand that it is extremely hurtful to receive negative comments about my children, or to see the angry looks shot at them and me, and I wish everyone would think of this when they see a family with young children at Mass. And if they bother you so much, offer to help (and by help, I don't mean offering to watch an older child while the mum removes younger ones).