You have gotten some great advice. I agree that the best solution is to go to a lifeguard.
I find it so hard to keep my mouth when it comes to badly behaved children in public. I'm a teacher, and in my school district, we discipline all children in our schools, not just our own students.
Whenever we are out, my DD will remind me that this is not my school, and she will tell me to walk away. I remember one time in Target, a child was rolling on the floor at the pharmacy then tossed a rubber ball to his brother who was running up and down the aisles. The mother was 3 aisles away ignoring her kids. DD saw my mortified face, grabbed my arm, looked at me, and shook her head, "NO." Another time when I was alone in Target, a child was in the dollar aisle looking for something and throwing everything that wasn't what she wanted on the floor. The senior adult with her somehow didn't notice. I nearly tripped and fell on the stuff on the floor. I went up to the child, and in my most stern teacher voice said, "You pick everything up right now! Got it?" And she did with the help of her Grandma. I quickly left the area just in case Grandma got mad.