Thanks for sharing your stories. Are both children gifted? Did they have any other "issues" (sorry to be so blunt I am just trying to figure out why she might be like this)? It does give me some home when people say that things may mellow as she gets a little older.
DD7 is MG+ and DS8 is HG possibly PG so far as I can tell. Both seem to have some level of sensory integration disorder. DS's behavior always seemed more troublesome because he seems to completely miss social cues and therefore getting him to learn that when someone says "Stop doing that." they don't mean "Stop doing that five minutes from now". DD has a much more social nature and she is really doing very well socially now.
It wasn't until third grade that DS's behavior became something that really effected him socially. I think as a kindergarten, and second (skipped first) grader the boys were all a bit rambunctious and prone to jumping wrestling etc. Now in fourth grade the parameters of acceptable (cool) behavior have narrowed so between his intensity and his lack of awareness regarding social cues he is judged pretty harshly.
I was really unprepared for my two to be so intense as my older two were "pieces of cake". But I have learned that it is important to do two things - 1. make sure they feel accepted for who they are at home and 2. they need a really firm set of limits and boundaries clearly laid out to help them see and react to those around them.
I sometimes feel like they are just so energized by their level of thinking and are eating up every experience with all of their senses and thoughts and that this is where the intensity comes from. I can't say that like some on here that workbooks etc. helped. Physical exercise with a large sensory component - like swimming - did help. Running and playing with other kids most often ramped them up to ridiculous heights.
Why are our kids like this? If I had a good answer - even an educated guess I would share it. Does your daughter's energy/intensity level have a cycle at all? I noticed that DS will seem to be calming down for five days or a week and then it will return with a vengeance. What I see at home also translates to school so it isn't changed by the setting. Last year his teacher and I often found ourselves asking each other on the same day - "What is going ON this week???"
Keep sharing and find a way to get a break! Teenage babysitters are great because they are old enough to handle most situations and are young enough and non-judgemental enough to actually have fun and play hard enough to keep these kids going!