The fact that you can't shake your feeling of mistrust is healthy, and a sign of self-preservation. You have good reason to doubt her and there is no reason to let this feeling go until you have the feeling that you are safe with her. So far you have no reason to feel that way. Why?
Because saying that she's sorry, no matter how sincere she is, doesn't guarantee that she won't misbehave again. What you need to hear is that she owns the fact that she behaved impulsively and that she is working to correct the problem.
Working to correct the problem would also involve addressing her drinking. Getting drunk and going out-of-control is a serious issue. Saying I'm sorry isn't owning the severity of the problem. She needs to own that drinking to the point of becoming drunk, and behaving in ways that are destructive to herself and her relationship with you are serious problems.
When people act out under the influence of drugs or alcohol you are dealing with two separate issues. One, is the problem of impulsiveness (if I feel like doing something, I do it). Second, the person who acts out when under the influence is often out of touch with many of his or her feelings, and these feelings'leak out'whenever self-control weakens, as is the case when under the influence.
She needs be working on owning her feelings and talking about them, rather than acting them out. She also own the fact that some part of her psyche thinks that it's all right to go out-of-control. When a person gets drunk and then misbehaves it's because he or she believes, on some level, that one is entitled to behave however he or she chooses.
Alcohol becomes the excuse for the behavior, but beneath this excuse is the belief, 'I'm allowed to do what I want.' If she doesn't identify this issue, and own it as a problem, then you need to concerned that she will give herself permission to act out in the future.
You need to have a serious talk with her. Saying that she's sorry isn't good enough, as your own instincts have been telling you. You need to see a sincere willingness to face her problems head-on and work on them. Your trust needs to be held in reserve until you see her owning and working on these issues.