I could have written every single word that you have written (and I have somewhere in the past threads).
Dd is nearly 3 and, to all intents and purposes, has never seen her father.
By strange coincidence, I spoke to him for the first time in nearly 2 years today. We have had a little email contact inbetween. I have raging PMT today (sorry TMI). I've only just realised and it must have been that that made me impulsive enough to call him.
I sent an email a month ago explaining that she was asking about and for him - got no reply. We had a reasonable conversation today (or it would appear so, on the surface, if I didn't have a wealth of experience of being disappointed and deceived in the past) and he is saying he is still thinking about having contact. He'll let me know in a few weeks (read months or never).
He has had three years to think about it. He talks about whether it might do more harm than good (he doesn't want her to get hurt by his unreliability?). What he really means is that he can't be arsed. Yes, he is thinking about it but I won't hold my breath.
Like you, I feel compelled to do whatever I can to facilitate contact between them. It would also make me feel a hell of a lot better if we could put the past behind us. (I hate feeling that I've brought a child into the world whose father doesn't care. I feel responsible.)
But, as others have said, even if you bend over backwards, prostrate yourself on the ground and beg and....???!?!??!!?...you can't make it happen. It is not our responsibility or choice, it is the fathers'.
I just have to try from time to time because, otherwise, it preys on my mind. For my own peace of mind, I have to remove any possibility of my looking back at this time and wondering whether..if....I had...then....????? That's all I can do.
Commiserations.