There is always a chance for things to work out down the road. But, you can't "show her not to be afraid." If she is frightened, she is frightened, and, from what you say, with good reason. Accept that.
You haven't said whether or not she is open to looking at where you are now. If she is, fine. If she's not, which I suspect may be the case, in the interests of any potential future you two may have, you need to let her be - and let her be in a loving way. Translation: Leave her alone, or whatever it is that she's asking for.
Abuse is about imposing your will on your girlfriend. This is often very hard for the controlling person to "see." Especially when she's had it and doesn't want to see anything. You are in a bind: if you let her be, you think that she won't have the opportunity to see how you've changed. If you don't let her be because you are convinced that if she would hang around a while, she would see the changes - you are doing exactly the thing that drove her away in the first place.
Your only (sane) option is to give her all the space she requests. Respect her feelings, whether you agree with them or not! At some point, she may realize that she's gotten space (gasp!) - and come take a look-see. Or, she may not, a possibility which you will have to deal with. Nevertheless, letting her be and respecting her feelings is the type of healing experience that can help ease her fear - and eventually restore her trust.
Your greatest ally is time, for not only will it take time for you to change, it will take time for her to notice your change - as well as to rethink her position.
As people start to change, typically, they feel as though they are totally different than how they were. Try to remember that as much as you may have changed, you are only at the beginning of a process of change. You will think that you've finally gotten it many, many times before your partner is likely to agree with you.
But, look at it this way: what else have you got to do with your time? Whether or not your relationship with this woman works, you will still be stuck in your own skin. You will take the same baggage everywhere you go, until you learn how to put it to rest. In the long-run, you can't lose by fixing up your broken pieces.
So, take your time and focus on the work you still have to do (its more than you think, I promise.) And, count your blessings that this woman left you. She gave you a wake up call that may benefit you for the rest of your life - and, good for you for hearing it!
I wish you the very best; you can do this. In the beginning, it feels more like you are "losing" than gaining, but after you begin to get in touch with your budding self-respect and integrity, those feelings begin to drop away.
I'm going to open this up for discussion. Also, please feel free to let us know how you're doing. Just know that I am 100% behind you and I am rooting for you! Good luck! Dr. Irene
I just want to read the posts.