Because of the possible hereditary connection, I sure wouldn't rule out the possibility of bi-polar illness, even if she's not presenting in the most usual way for her age group. But here's another angle to explore:
There are many, many chemicals that are part of our everyday environment that can affect mood in children and adults. Most of these chemicals didn't even exist a few generations ago, so our bodies are not adapted to them.
A very large and well-controlled British study a couple of years ago confirmed that not only several common food colors (two of which are banned in the U.S.), but also the preservative sodium benzoate made hyper kids measurably more hyper. See a report here: http://www.consumerhealthreviews.com/articles/GeneralHeal...
There are also other sensitivities/allergies that make children physically or mentally uncomfortable and hard to please. She might be sending out signals for help, but have no real idea why, if she's just always at odds with her own body.
I have severe chemical sensitivities, and get both physical and emotional symptoms to exposures to perfumed toiletries, home cleaning products, fabric softeners and air "fresheners." (Many of these are just downright toxic.) In group testing situations, I have watched children go from contentedly coloring to bouncing off walls, screaming, crying, or being impossibly stubborn just minutes after having drops of some dilute solution squirted under their tongues.
It would be worth checking out. You can try sealing all suspicious products in plastic bags and using free and clear detergent, baking soda or vinegar for most cleaning for the next 2-3 weeks, and watch for any improvements. If reintroducing the products back into the home then results in worse behavior, you'll have a possible solution to work on.
I know this sounds like a lot of change, but it's really not that hard to try. Most of the household products and toiletries commonly used are really not needed, and they are expensive. We believe we need them because the advertising is so compelling. But I've used very little for cleaning in my home besides baking soda, white vinegar, borax, hydrogen peroxide, and scent-free detergent for over 20 years. My house always smells clean and pleasant – and visitors often remark that the atmosphere is "calming." I think their bodies are noticing the lack of toxins in the air.