Well, her reaction was pretty understandable at the beginning, after all she ended up in some sort of fantasy-alien world, away from everything she knew and loved. Her threatening Henry and trying to get a rise out of him, is probably a defence mechanism to try and get some control over the current situation. Combined with her being a teenager and coming from a world of free-spirited people, it is pretty understandable, albeit stupid, that she is doing all those things right now.
Saito, IIRC, tried to escape from the Academy in the beginning and when caught by Guiche, he knew he needed to bind for time until he could get away from these people. Anne, OTOH, is a bit more emotional, because her personality is wilder than Saito's more subdued character and she is what I would call a person of action, living every day as if it were her last and screw the consequences of her actions. Frankly, I think she would be more suited as Gandalfr rather than Myoz, she just doesn't seem to have the patience to achieve her full potential.
Also, why does everybody think Agnes is the best candidate to teach Anne? The only thing it would achieve is her getting even more frustrated with Halkeginia and alleviating everyone around her, possibly making her a greater threat than Sheffield, if Reconquista can manipulate her into helping them.
What Anne needs is someone to stay by her side and try to explain what is going on. Henry is possibly the only person that can achieve that, thanks to both his resurrection status, making him more empathetic towards her and his charismatic ways of making things seem better than expected.
An example would something like: 'Hey, you are the Mind Of God, which gives you the same abilities that every noble has at your beck and call. You can achieve your childhood dreams of shooting fire and melting people's brains with your mind, being a superhero and all that. You are also the familiar of the leader of one of the most powerful countries in the world, which gives you more leeway than what you would normally get, even as a noble. Lastly, you can pretty much inherently understand everything that is magic in this world, maybe even find a way home, hint, nudge'.
After that, she only needs a good magic teacher, maybe as a student at the Tristain Academy of Magic? Or even a private tutor, like say Charles, to mend the brothers fractured relationship perhaps.
Again, these are all possible scenarios, but we just have to wait and see what Henry will do to fix this.
