Somethimes women will imply things but won't say them sometimes they like to be chased it makes us feel wanted and needed imnot saying that its right but I do know its true. She probably deep down wants to be back with you and I will go as far as to say she is probably crying at home when she is alone she mentions your name to friends or people because she is hoping someone will say something like yeah I saw him out with so in so so she can resort to anger and that keeps us feeling strong. I think if you really want her back make a grand gesture. Its clear that you both have faults and they should be wel thought out and discusses try something like sending her flowers and attach a list of things you acknowledge you need to work on and at the bottem ask her to make a list as well you will both have time to review and them maybe meet for coffee to discuss how to fix the issues and have a fresh start remember being honest in the beginning will save you in the end.