Do you think she's acting like a teenager in a substantive way, or just in her style?
I like her irreverent attitude and I don't consider that childish. She doesn't act impulsively, thoughtlessly, or disrespectfully. She takes her job seriously. She intentionally goes against the grain of traditional military stuffiness because she is decidedly not trying to train a military.
The underlying military culture of classic Trek made sense at the time, but we can do better. I'm actually optimistic about SFA and that's almost entirely thanks to Hunter's portrayal of Ake.
I agree with what you're saying; I just don't see it in Ake's behavior (perhaps because I am a few episodes behind).
I haven't seen her behave irresponsibly or take the safety of her students lightly. Lounging and going barefoot are not safety issues, unless you consider all forms of unconventionality to be unprofessional, and all forms of unprofessionalism to be irresponsible.
What I see in Ake is someone who takes her job seriously, and is conscientious about what deserves her care and attention -- and what doesn't.