We parent the same way and have similar kids, OP. And we had the same issues with the school. I love how they told you you're hothousing and then suggested you do a math curriculum at home.
I would definitely get IQ testing, it measures potential, not achievement, so it will bolster your point that you have not pushed her. But don't expect it to be the magic bullet. They might be quite capable of saying "1 in 50000 IQ? Still needs to work on handwriting and focus in class". We were the only ones surprised by the test results. The teachers who'd been stalling us knew the order of magnitude of the issue.
I stress that I want my child to learn to work hard, that doing well in life requires application, focus and resilience, which you don't learn by sitting at the back of the class with a novel. You learn it by doing things which are at the limits of what you already know, and sometimes failing at them.
And if you're already paying for schooling, I'd look around for other options. Our problems were solved by finding the right school.
Good luck!
