Get over yourself. Really. Yes, I realize that your kid is precious. Mine are, too. I also realize, however, that my child is going to learn to overcome physical obstacles and further develop her gross motor and social skills from the manner in which she plays on the tower of fun that rises above me, while yours is going to learn that her mother is a stuck-up psychopath who too easily gets her panties in a wad. Which is the better lesson? You decide.
Lay off a little, lady. When my child teaches yours to roll across the floor in a tumbleweed-fashion, don't snatch your daughter up, brush her off, and proclaim, "That's nasty," with a wrinkled-up nose. I mean, come on! You can give her a bath later. Don't shoot me disdainful glances when my daughter hops and jumps onto the slide. She didn't hurt anyone and may have learned a little bit about gravity. Just let the kids be. They will have more fun, I promise! And, they won't even kill themselves (at least, it isn't very likely).
Playgrounds should be places of fun and laughter. Coaching parents need not visit. Don't you realize how obnoxious it is when you stand to the side, yelling at your kid to perform like a circus donkey? Don't you think it might even embarrass that child just a little? Let them be kids. Let them pull themselves up to the highest parts of the mouse-maze of delight. Let them sit on the end of the slide. Natural consequences might dictate that they don't do it too terribly often. Likewise, don't push them to do things the "right" way. You may just stifle their creativity and self-confidence.
Relax and go with the flow, man. Next time you visit, bring a book, some headphones, a bag of needlework, or a friend. Give the children room to grow in their play. Allow them to explore and don't panic if they get a little boo-boo. Hey, shit happens. It really isn't the end of the world. Besides, they might learn something from it.
The crazy lady who lets her kids run (semi) free