S.M.
Hi Sumi,
I am the parent of two toddlers who go to daycare. I have to say that I have seen a progression in the way they interact with other children, and each other over the past two years (still requiring frequent interruptions by mommy and daddy not to sit on your sister, pull hair, and to share). Some days are better than others, for each of my girls (2 1/2 and almost 3 1/2). Sometimes they play so well together I am absolutely amazed. That said...On any given day at day care, or in the park, you have a mix of kids at all the stages of socialization/communication, and in all the moods. Complicating it, it sounds like your little girl is used to only dealing with her own moods, and understandably expects everyone to understand what she understands about what is right. My younger daughter (by 10 mos) went through a period when she hit or bit as a way to protect what she thought of as hers from her big sister and the bigger kids at daycare. This was when she was preverbal and couldn't really speak-up for herself very well, but it took A LOT of work to get her out of that behavior. She still plays rough, not mean, she just likes to wrestle and doesn't know when to stop...As the mother who has stood exhausted and frustrated watching one child get down the toddler slide, while the other gets into a scuffle with another toddler at the top of the slide and bends over to bite him, I expect and appreciate the help of any other parent at the lot who reinforces the "we don't bite...say, sorry and let him down the slide in front of you" rule. Most of the time I could stop her before she made contact <g>, but the lesson would stand - you cross the line, you lose what you were arguing about. Anyway, I would also help the kids "figure out how you can take turns," etc. If your daughter sees you stepping in to help her solve the problem that started the issue, it will teach her some problem solving skills, and how to get along better "in the crowd." This should lessen her anxiety overall, and hurt feelings specifically. It will also help her when she goes to school and finds those same kids there.
With regard to approaching another mother, I wouldn't approach another mother unless my child hurt another child (by accident or design), or your daughter was actually hurt. But I would hope that if your child was bleeding, and you were making enough of a fuss at the playground, the mom would show up.
Best of luck.
S.