When teaching kids about shul, you must teach them the rules of the shul and that the shul is a special place, a place we go to speak to Hashem and ask him for special brachas. The special needs child is taught that and that is why he gets great pleasure out of being a part of the shul experience. HE understands that it is special to be at shul.
Young children can understand that but only appreciate that for a small period of time and then they lose patience. So they should be allowed to come, but only for the amount of time they can sit quietly and enjoy the shul experience. Obviously as they get older, and their attention span increases as well as their ability to read Hebrew and participate, they will be able to stay longer and enjoy it more.
However, to expect the father to “watch” the children in shul while he davens, so MOM can get some rest at home, or prepare lunch without the kids bothering her is not a solution. To bring the kids to shul because they are just so cute and doesn’t everyone want to enjoy your kids as much as you do, is just plain outrageous. And to bring the kids to shul so they can absorb the atmosphere and somehow just feel the kedusha doesn’t work either. Chinuch needs to be really thought out and planned. And you can’t ignore the fact that you are teaching a positive thing on one hand while teaching a very negative thing on the other. The negative being to have the chutzpah to ignore the people around you that you are disturbing and the kavanah that you are literally stealing from them.