In reply to Hungary Bill (Forum Supporter) :
Also... not a parent, but... I did teach 4-8th grade for several years.
Precocious and clever kids like this can be a bit irksome, but far less annoying than most. Usually it's the frustration of them being too clever to really punish much because they've learned really well when they can and can't push it and how to walk it back. They know better than to fight you and challenge you strait on. They were some of my favorite kids to teach.
Montessori might be a really good fit for this kid.
Edit: We had a family trio that your situation reminds me a lot of.
Eldest was a very boyish boy. Most prone to outbursts and "trouble" of the three. He was also one of the simplest and most direct to deal with. He knew when his behavior was wrong and it would just be like, "You messed up. Go sit your punishment," and he'd go do it very matter-of-fact. Best way to head off trouble was to get him moving to proactively burn up his energy before it bubbled over.
Second reminds me a lot of your elder. She was the easiest to deal with and sort of the theoretical "model student". Relatively quiet, easy-going, simply agreeable.
The youngest reminds me of your younger. Oh my lord was she clever. Both maddeningly and impressively. Things was, you almost didn't need to manage her because she was going to manage herself... and everyone around her. Whatever it was she ultimately wanted to do, she'd navigate the situation to make it work for her. When she started to misstep, you could basically give her a look, she'd smile puckishly, back off, plan, and change tactics.
Having dealt with her, the advice I'd give is, don't fight it. Trying to stop her from achieving her goal would have been a losing proposition. Frankly, what she wanted wasn't ever really a problem. All you had to do was sort of set some guardrails and boundaries, make it clear where the hard lines you wouldn't compromise were, and then she'd figure out what was best for herself.
Eldest and youngest both medaled at the California State Science Fair. Eldest took a 1st place for Junior High one year. Youngest won a special award or scholarship thing for promising young women in STEM.