I am part of a formal playgroup and have been for quite sometime. I have no issue with, I wouldn't say disciplining other children, but I will step in if there is a need to for example a) the parent isn't around / doesn't know what is going on or b) is standing there letting their child throw sand/be mean to other kids (had this yesterday at pg) etc.... I certainly don't yell/touch the other kids etc.... but for example, there was one child about 4 yo who wasn't letting other kids go down the slide - the mum was there but I don't know if she knew her son was being unfair to the other kids, so I asked him to move - he then gave me attitude (said no! and come up with some reason) and I told him to move out of the way for the other kids, so everyone can play. I would be ok with another parent saying this to my DD. The thing is, I watch very closely to where my DD is and what she is doing, so if I need to step in I am there fairly quickly. Maybe this is a bit of overkill, however we have up to 25 kids at our playgroup and it gets hectic plus there are some babies (8 mo) there and sometimes the older kids are running around crazily and it gets concerning for the younger ones.