A subject we've spoken about before is taken up at NCR.
Been there, done that as a parent with small children. There's no question, it's tough. But with some planning, most children learn quickly that this is an hour when immediate gratification is not available to them and they can be limited to one or two quiet interactions.
There's always one family Mass at a convenient mid-morning time. Everyone who goes to that Mass either has small children themselves or they've disciplined and refined their prayer life to see and hear above what is human. You'll feel right at home.
Buy a small/cheap backpack or tote for each child and keep it filled with things that are only available to them at Mass. Coloring book, crayons, a couple of books and small figurine toys that inspire the use of their imagination. Keep your eye out for sales on toys or crafts that inspire imagination and switch it up every few months. The limited availability of these things keeps them interested. I also packed a snack and drink for each of them in their bag. (Craisins/juicebox type of snack.)
It's helpful to also take them to visit the Blessed Sacrament outside of Mass. (If your parish has First Friday Adoration or you're lucky enough to have perpetual adoration, even better.) Explain why we reverence the Body, Blood, Soul and Divinity and our sacred space with silence, and need to respect the people who are speaking to or listening to Christ. Do it a couple of times a month, stay for ten or fifteen minutes.
Infants need to be topped off with nourishment prior to leaving the house. That includes breastfeeding Moms. A woman who doesn't know how to manage the nourishment of her infant so hunger pangs won't upset their equilibrium, so she can run to the grocery store, etc., has emotional, intellectual and/or other problems that I'm not going to get into in this post. Suffice it to say, a woman never uses the Sacred hour to breastfeed. If you are running late and don't get the chance to top off your child, take 3 oz of water in a bottle. (No more than three ounces and nothing but water because the success of breastfeeding relies upon the substance and rhythm of demand. Never decrease that demand, except for an emergency and only with water!) If a circumstance presents itself that has thrown the appetite of your baby off, and you realize you have inconsolable crying on your hands - pack up (with all your children in tow if necessary), excuse yourself from the pews and find a private place to breastfeed your child.
Motherhood is all about planning ahead and executing the plans - a work of art and beauty. Some women are naturals. Some learn along the way. As women, we should always have a handy supply of patience, kindness and support for another woman struggling with this balancing act. If you're in a place where you can't (and I understand perfectly the many reasons why a Catholic may need or want the quietness for these great and holy moments) - my recommendation is to go to the 7am-ish or 6pm-ish Mass. These are two Masses that most mothers with young children can't attend - so you'll be somewhat safe.
There IS a problem with parents whose children are undisciplined and unruly for a multitude of reasons. The economy has enslaved the family. Exhausted parents who pick up their children from day care centers, don't have the bandwith to parent or they struggle with guilt because of the situation and can't bring themselves to discipline in the precious hours that remain in the day. You're not doing yourselves (or your children) any favors by avoiding discipline. If your children are not reasonably responding to the above, you're going to have a problem when they get into school - perhaps for their whole lives. Not coming to Mass really isn't an option. For them or for you. Better to take the bull by the horns and reign it in with help of the mystical and the Sacraments going on around you week after week.
With all of my attempts above, even I was driven away for months by a nasty encounter. We are a community whose fiat is service. Every once in a while, I come across a story from a young parent that tells me we are doing a terrible job responding to their needs with patience and charity. I worry about the fruit of their discouragement - especially if their faith is weak.
May Our Good Lord bestow abundant blessings upon young Catholic parents.