Regarding language, you would want an evaluation done by a speech language pathologist. A related possibility would be an auditory processing disorder (evaluated by an audiologist), which might not show up as affecting language when the language is in print, but could very easily affect how she receives language when it is spoken, especially in a busy environment, like a classroom. This, by the way, often is part of the diagnostic discussion with ADHD, as there is much overlap in their presentation. Alternatively, (and more like her testing) she may understand language very well, but have more challenge expressing herself. This would affect how she communicates her feelings, organizes her thoughts, both when speaking and writing, and feels about writing assignments. It may be worth investigating if that is also a contributor to her impatience with writing.
The gap between handwriting and other academic skills is a classic "too easy/too hard" situation, since so many of our educational conventions require written paper products, even when the ostensible learning goal has nothing to do with handwriting or written language.
