Daughter gets discouraged easily

My 9 yr old daughter is dare I say behind in homeschool math and writing. I think there is a direct correlation with her attitude problems when challenged. Her reading and comprehension skills on the other hand are exceptional…she has read all the books in the house, sans the adult books, and we go to the library weekly. She can cook and bake from recipes and enjoys history. She is the eldest of 5. When her younger brothers are working on something she has previously found difficult…she will say how easy it is. It seems to me that she feels she has to dominate in intellect since she is older. My husband and I both agree that it may benefit her to get a formal ADD diagnosis. What are your thoughts on this? We do not want to medicate, although I do want to help her understand how her mind works and what challenges she may face and how to persevere. She is very easily distracted and forgets simple instructions often. I’m realizing as she gets older how much she struggles with this compared to her brothers and peers. When she doesn’t understand something she can be quite mean. I’m trying not to take it personally. I guess my question is how to instill intrinsic motivation into subjects she finds difficult, thoughts on ADD, and when to worry about her getting agitated easily, and when to worry about her trying to control her brothers (eg…calling them names…like literally a name that is not their when they don’t think it’s funny, often leading play, telling them want to do etc.).
Thank you!!!!