Your first point: It isn't like he wears a shirt with the words "I'm a crazy mother****er" embroidered on it. His issues aren't clear to anyone but Angie, Barbie and his dad. Her eyes are probably open to it now, post-gunning down that rapist hick.
Your second and third: Her choices were selfish and emotional. She's not a braindead idiot, though. Considering who her coworkers were when the dome went down, I'd say she is the second most intelligent member of the Chester's Mill PD, after the poor bastard who took the bullet that ricocheted off the dome.
Plus, you know people in positions of power never follow their own rules.