At least from your description, your daughter is acting very normal for an early adolescent. The babyish behavior is telling you that she's not sure she's ready to grow up. She still requires the assurance that you're there for her. If the behavior is too childish, like temper tantrums when she doesn't get her way, you can ignore it and discuss the issue at a calmer time.

If it's simply fearful childish behavior, you can help her by being supportive and encouraging by saying, "What's the worst thing that can happen to you if you go to the party and you feel a little left out?" or "What can you talk about to start a conversation?" or "I remember being afraid when I was your age, but it got better after I tried it once or twice."

The overly-mature behavior can cause greater problems. When 11-year-olds want the privileges as 20-year-olds, it's time to hold the line. Your daughter will not appreciate your limits now, but she will eventually. Try not to talk down to your daughter but do be willing to say no firmly when you believe a request deserves a no. In case she accuses you of always saying no, remind her that the real world will give her many no's, and there are no better people to learn to accept no's from than the parents who love her. Patience is an important quality to teach your daughter at this time. Learning how to think through and project future consequences will help her with her problem-solving forever.

At age 11, your daughter is just beginning the exploration of her path between childhood and adulthood. It can be a most interesting time of child-raising, and it doesn't have to be the ugly time the media has painted. Take time to listen and talk with your daughter as she explores her new pathways, and think about that time in your own development, so you can thoroughly enjoy your relationship with her.