to the original poster, though, this personality is tough and I agree with using humor as much as possible and to start thinking of it in terms of learning strengths and challenges (like low threshold for tolerance) and the more you get to understand her, the more you'll be able to figure out how to help.
And the role playing idea above I think is really helpful. Do you think her ideas for playing are more complex and intense that her peers? You can keep trying to meet more kids and try to not worry too much about the parenting thing.
Some parents of easier kids act sort of smug, maybe they don't mean to, but I'm sure you're trying your best and are always seeking new things to try. Just try and relax (easier said than done) and be proud of yourself and it might help your interactions with your DD. One of the nicest things someone said to me once when DD was being especially intense several years ago and they watched me trying to deal with it was a dad who was there said "phew - that's got to be a tough personality to deal with, you handled that really well!"
Of course the feedback isn't usually that encouraging or understanding...
Try to not always make it seem like it's her fault when you talk to her but that she has to learn about herself and how she can navigate people in the world. She might already feel different that her peers and that's part of her anxiety. You could get her to try and talk about how she feels when she plays with different kids.
If it happens on a playdate and you can intervene, just ask her to stop and think of the other child's idea or have them take turns for how to do things. It's helpful to make it "cognitive" as much as possible and she'll gradually get better.
