Is there a box of 'stuff' for children attending Mass? Apart from crayons and (Catholic) colouring sheets put in the entrance, maybe some soft cars (you can get brightly-coloured toy cars made from soft rubbery material), other quiet but fun toys (we used to have some rubbery Power Rangers!), some books (Bible stories or saints or about the Mass, with bright pictures).
I've found this book is good for keeping young children quiet amazon.com/Sammys-Fantastic-Journeys-Early-Heroes/dp/0840791615
For children closer to learning to read, or who can read but haven't yet started receiving Communion, I find this book excellent amazon.com/Little-Missal-Including-Translation-Childrens/dp/1860825656 It lets them see where they are in the Mass, and also has lots of bright pictures with a lot of detail. It explains what is going on. It doesn't have all the words, so a child who is receiving Communion should probably be using a fuller order of Mass or missal.
Maybe if there was this welcoming collection of special church things to look at and play with, it would be easier for the family? You might be able to get the parish to fund such a thing, as a general resource for all families.
Also seconding the suggestion of a children's liturgy, if you have the people to run it.
We never get to know the full story of any else's life: I know that after my youngest brother was born (the fifth child), our family became a much more stressed group, for reasons that aren't as simple as how many children there were. Some people in the parish were ever so kind and helpful, in ways they probably never expected when they offered to help! But we could have done with so much more support, and we were all quietly miserable and struggling to cope for years. Some of that was to do with how little support we had from extended family. Yes, some families with more children sail through with impeccable manners, but you don't know what this family is coping with. The priest probably knows a little more, and won't be telling you any time soon.
And yes, it's hard for you to cope with so much noise during Mass, and obviously you should be seeking a solution (as you are doing). I'm just saying, try not to be judgemental about the family. We only get to see the surface of what is going on.