I think if you posted a notice that said "All disruptive customers will be removed from the premises. This include children." that most people would approve of

I think if you posted a notice that said "All disruptive customers will be removed from the premises. This include children." that most people would approve of it. A few people with noisy kids would object, but that's who you're trying to get rid of in the first place. You would have to actually enforce the rule, and that would be ugly, but it would have been way, way less ugly than what's happening right now. And it would have been just as good for publicity, if you advertised it.