Guess I'm in a bit of a different camp on this issue--or should I say issues? Ours is a very large guild with monthly meetings that draw about 60 people. We have an expectation that the monthly meeting --both the business portion and the program, be easily heard by all members. Since some of our members have difficulty hearing, we have no problem of reminding about no cell phones going off (if you need to take that call, then please step out of the meeting room) no loud side conversations or other disruptions--including children. We don't say no children because as someone else said, during the summer we often have g-mas or moms that have to bring a child or forget about quilting. As long as the child is quiet, it's not a problem and everyone is respectful of that.
We do have a paid membership and we WANT children to become quilters--so we have a reduced fee membership for them. We also have a 1 day workshop in the summer to make a kid-friendly project (potholders, tote bag, pillow, etc); have had a kids' corner at the annual show (usually with the child making a take-home project and also a charitable project) and jr. category at the show; and have several jr. members--as young as about 9. In our beginner classes we've had several 4-8th graders--they do fine.
I guess what I'm saying is that you seem to have 2 issues--noise/disruption vs children being involved. Our workdays are for members only--so if you enforce that with paid memberships, doubt those moms will pay for their child in order to drag them along! if your officer board is in agreement about it being a problem, perhaps the first step would be to have an officer speak privately with the guilty parties and explain the concerns.