...admittedly I made a mistake by moving out but I just don't understand (rationally) why W won't let me move back in.
I don't want to sound overly critcal, but read that a few times, and tell me you really believe it! You moved out on her, on your terms, and now you want to move back in, on your terms. Why would she want that? Put yourself in her shoes. How does she know you won't change your mind next week, or next month?
As far as rebuilding living apart, well, you built it the first time living apart, right? How did you do it then?