Christopher Elliot has a nice piece on loud children on planes, suggesting planes ban parents who have proven to let their children scream. Elliot admits that after his first plane trip with his three kids, he realized he couldn't control them and grounded his family. That's a wonderful sentiment and I wished more families were as concerned about their externalized costs as Elliot is. But it's just not a practical solution. Suppose a family emergency necessitated speedy travel: would he still refuse to fly? I doubt it. Therefore, the optimal solution isn't a corner solution.
Instead, we could use a Coasean solution (well, Coase-like since transaction costs are too high for full bargaining and we're not focusing on the least cost avoider). Airlines would amend the agreement when you buy the ticket (which already includes clauses about when you can cancel the reservation, etc) to include a provision that if the stewardesses feel your child is too loud (perhaps in part based on customer complaints), they charge some additional price based on the length of the flight. To prevent the company from saying anything is too loud and to compensate those suffering from the screaming child, the airline then reallocates that money to those in the seats nearest the screaming child.
This system punishes those parents who don't control their child (generating the incentive for them to be better parents or avoiding flying altogether) while still allowing them to fly if they feel circumstances warrant it. The costs to the airline would be small since so much passenger information, including credit card numbers, is in their database anyway. But it's not zero, so there's an incentive to not report every little scream as a violation.