What a wonderful problem to have! At age 39, I am one of the very youngest members of my guild (and I've never had children). On special occasions, people will bring granddaughters that are interested in quilting. They pay a guest fee for those children to join in & the kids (typically at least 10-11 years old) work alongside their grandmother. Those ladies get less done on those days because their focus is on spending time with their granddaughters. I hope to bring my niece to one of those sew-in's sometime this year. She is turning 5, but will patiently work with me on quilts usually for about 30 minutes at a time, provided we're not just doing one thing for 30 minutes. I know I need to plan to take breaks with her & even during those half-hour segments to keep changing what we're doing (drawing our design, picking fabrics, cutting out the applique shapes, layering piecing pieces, inking fabric, picking thread colors for FMQ & so forth) and stick to making something that's no larger than 24"x24". I don't plan to stay for the entire time; even with all that, we'll probably leave around lunchtime. I basically get nothing done when I work with her (or even with the 9-10 year olds I've taught to quilt). We work on her little quilt & that's it. I can't imagine trying to take her to a lecture-style meeting.
As a former teacher & nanny, I don't think it's typically reasonable to ask that children sit quietly without anything to do. Young children generally will sit quietly if they are actively engaged in a task & there is a new, engaging task roughly every X minutes (X= the child's age). For example, a 5 year old will typically be actively engaged in a single task for 5 minutes; after that, they will start get bored & it's only a matter of time until they start looking for something else to do, perhaps in a disruptive manner. It's not usually until the teenage years that the brain is developed enough to focus on a task for a longer period of time (and sometimes not even then).
Perhaps you could include some of the members who are parents of younger children in the decision-making process. If you explain that the Board has noticed that there are a number of young children coming to the meetings/workshops & you are looking for a way to make them feel more welcome & included, they may come up with a solution no one else thought of. You can bring up the safety issues (if any), or the fact that you know it's a lot to expect them to sit still and listen to an hour-long lecture (if that's the case), or whatever the case may be. If they are quilters, maybe give them a chance to share their quilts during show-and-tell time. I've seen instances at workshops where some ladies were frustrated that they didn't get to "quilt in quiet" warm up to the idea of working alongside of "noisy" young quilters after seeing a 10-year old girl proudly describe & present her project.