I would not have been okay with another parent yelling at my child for something as petty as a hat getting knocked off. They are 4 year olds and like to play around. I'm sure that the hat getting knocked off isn't going to cause as much damage as her reaction. I would go to the coach and the league commissioner and have her warned so that she understands that kind of behavior is unwarranted towards any child regardless of the situation. How would she have reacted if her child had knocked your child's hat off? Most likely, her child is a "do no wrong" type child and she rescues it from every unattractive situation no matter how large the issue. I think if a child's safety is in jeopardy there are ways to get the child's attention without yelling or acting like an immature fool. But, a hat getting knocked off a child's head is not as dangerous as say letting them stand in a ball field and have balls hit at them. Good luck for the rest of the season!