I think that you maybe need to pick your battles. If your child is in a position of actually getting injured or worse by bigger kids, then it is your job to step in and remove your child from the situation. However, if it is just about children not sharing, I think that your roll is to coach your child from the sidelines. When she comes to you crying because another child took something of hers, this is your chance to say, "Go and ask for it back and remember to say, Please!". If another child is pushing, you should remove your child from a situation with physical contact. So this is your chance to take your child aside and say, "It is wrong for that child to push you. When this happens, put your hand out and firmly say, Stop pushing me, and then walk away." If another child is being rude, the next time your daughter comes to you, you can say, "That child was not being polite, and I know that that must hurt your feelings. Next time that happens, you can stand up for yourself and say, Please don't talk to me that way, it hurts my feelings." Try and look at your roll as a coach. You can't play the game with her, but you can teach her how to play. Our children need to learn how to handle these situations on their own and stick up for themselves. Plus, your child will know that you have been paying attention, and that ultimately she has you on her side.
I think that this is actually more about your relationship and roll as a mother to your daughter than worrying about other peoples kids. Every situation is an opportunity to teach and coach your daughter, so that she can stand on her own two feet, rather than protect her and fight her battles. However, if she is in physical danger, you need to step in!