You D is 13 or around there? Ohhhh ho ho... I was EVIL at 13. The hormones rage and NOTHING is fair and parents are uncool and embarrassing. Keep in mind that this situation is landing on top of a difficult age for your D. I promise - It WILL pass.
Four months seems like a long time, but it could take until she is 15 or 16 to level out and see clearly. Your W isn't going to do everything perfectly in your D's eyes, either, so your D will eventually have enough evidence to understand that no one is the bad guy here.
Don't look at what your W is doing. Keep doing what you are doing and keep the faith. Don't watch the clock. Just decide that you are a better man for the rest of your life. A point will come at which no one can deny that. You will be embraced again.
A father is extremely important to a girl. You are her first definition of a man. By moving out, she will feel abandoned by you no matter what your W has done or how your W feels. Your D will be angry with you no matter what. Please be patient and take her painful cuts and jabs to show her that you will not *really* go away. That you are her dad no matter what, and that you love her no matter what. Be her hero. You almost have to be godlike, I'm sorry to say -- that is a tall order. But, you have to face the pain of your D's rejection and show her that you will always be her rock.
I know you're angry at your W and confused by her reactions to you. Just let her be for now and keep shining.
I hope that helps. I know you have to go through your anger and pain in your own time. You will feel better in time.