You say you don't want to push her away. You want to trust her again. You want things to work out... have you told her what she needs to do in order to start working things out? What are the requirements? You don't need to share any feelings about yourself, but I don't see any harm in sharing what you need from her BEFORE you can consider getting back together. I have yet to read anything about her working on herself throughout this time.
My interpretation of her emails is that she's looking for some action and she's looking to get it from you... but she's not remorseful for looking elsewhere and she hasn't even begun to fix the waywardness inside of her.
