I'll offer a few thoughts. Hope it doesn't offend.
Daughters who are sensitive... they hold it together in the outside world but when they get home (the "safe" place to be themselves) they let themselves go and show their frustrations and anger about. I'm sure you know this already. But more than anything at this point in time they would like someone to tell them they are still lovable and wonderful.
Also, many gifted girls are very sensitive. But yes when hungry, lack of sleep, or tired, can get very irritable. She doesn't want to be this way but probably doesn't know how to help herself.
I've been showing my child, as gently as I can, how she can recognize her own behaviors. "I'm starting to feel frusterated..." and I'm teaching her to say "I am frusterated because..." then what she can do to manage it. Go doodle for a while. Lie down. Ways to calm down.
Even a mildly gifted child in Gr. 2 doing Gr. 2 work will find it extremely frustrating and mind-numbing, I can't imagine how your daughter goes to school every day. She would need more differentiated curriculum work. Also, what do the other girls in her class/friends talk about? Deep issues about life? Or the latest tv fads and clothes? What books do they read, her friends, vs books she reads?
If this has been happening for any length of time, it can get anyone depressed. (Not to minimize your situation...)
I have to run... but having the professional experienced with gifted children will be helpful. By the way, if your DD is gifted, the parents are likely also, and other relatives. The sister may also be.
Also, girls learn to hide their giftedness very well early on in the public world.
