Teaching a first child

My eldest daughter is definitely the type "A"/leader personality. As the eldest of two parents whose placement was the same, we assumed that Cecelia would tend toward this personality. After all, she is our daughter, right?
Well one problem with first children is the fact that they often assume responsibilities that are not ours to worry about. I remember tattling to my mother about something my brother had done wrong. Mom would tell me that she could be the mom and I could let her catch my brother doing something wrong without my vigilance. In my head, I responded to her: "but you DON'T catch him doing something wrong. There are times where you miss something. I am just trying to help."
Alas, it is with this logic that many first children attempt to be their parent's little spy.
Of course, the logic is all wrong and the fact is that mothers don't need spys. There is a wisdom that mothers have about how often they need to attend to a specific problem. In addition, there are only so many rules that should be vigilantly held.
So... back to Cecelia...
She began coming home from school with a very familiar problem.
At first, it was within a couple days of beginning school. She slumped into the car and said: "I had a horrible day." Upon further inquiry, she indicated that someone had called her a liar. Of course, any parent would be upset and disturbed by this revelation. She told me that some kids were exchanging snacks and the teacher had a rule about how that was not ok. She told this group to stop because it was against the rule and they said "you are a liar".
So, the fact was, she was sticking her nose into another person's business. She felt it was her duty to right the wrongs and thus was seen as a rule thumber.
Then, another instance happened when a kid pushed her in line. She told the teacher and she was certain that the teacher did not address the issue to the kid.
Soon, I started seeing the pattern. She felt that her teacher was not catching every issue and wasn't responding when she tattled. Although I'm certain that the teacher did address every issue and that my daughter simply had not seen it, there are so many issues a teacher has to deal with.
So, we sat Cecelia down one morning to give her a new perspective. My husband explained how he struggled with the same feelings that she is now. He gave her a new idea. She was only supposed to be responsible for herself. She didn't need to worry about what other kids were doing or whether or not they followed the rules perfectly. She was not to tattle to the teacher unless there was blood or if someone was asking her to cheat. Her responsibility was to only focus on herself and how she followed the rules. We told her that there will be people who break rules. There will be times when a teacher cannot see it and/or when a teacher doesn't address things as we think they should. However, she has to not try to find those instances and when she does see them, she needs to not worry about it. She only needs to ensure that she is following the rules.
That day, she hopped into the car with a smile. I asked how her day went and instead of the typical gripe-list, she said: "great!!!!" I asked her how the new perspective was and she smiled at me. She said: "It's great mom. I only worried about myself and I didn't even see anyone do anything wrong. I didn't tattle all day." She immediately told me of all the fun things she did and all the new things she's learning. Instead of the long list of infractions that others were doing, she simply was happy.
I was so thrilled to see our idea work on her. Hopefully this will help her retain the friends that she has and help her to be happier.