It's tough to say what would have been the best thing to do in that situation. I usually hover somewhere on the line between the "let the kids work it out" and "try to super-politely boss someone else's kid around." But I did notice that you mentioned the mom had a sleeping toddler on her lap. Maybe the toddler and the 4-year-old had been running her ragged all day and the nap (that happened to occur at the park) was the only break she was going to get and she knew it. I've had days when sometimes my parenting standards are not as high as they could be and I let things slide, because I've just had enough and I need to sit for awhile. Granted, the public wading pool is a pretty poor place to do that. No graham crackers and cut-up grapes were required. But I think it's probably a good thing that you were patient with this kid--and by extension, her not-on-the-ball mother.