I agree it's OK if others correct my kids as long as it is in keeping with our values. We like to keep the positives rather than don't push or NO! If another person has to address my kids I generally like to follow it up - usually if you walk over and say something to your child like" ... what are you up to" I find most parents are quick to jump in with a "they were just having a squabble over such and such" which gives me a chance to reinforce with a gentle reminder like ... we share our toys. I will usually hover around and see if it's solved and if not either work through it or we will remove it's it's causing too much trouble.

More often than not I find I am the one dealing with other peoples kids as I find a lot of parents in public places like parks etc tend to turn a blind eye and ignore obnoxious behaviour. Which as others have said, I will usually just have agentle yet firm talk to them keeping it in the positive.

I am also a bit of a fan of letting kids work out things themselves once they have had some modelling/role playing how to share and stuff, I think if there is constantly a adult in the midst solving all the problems kids don't get the chance to experience things themselves