In my opinion, your child needed, and still needs, you close to her. Looking back on whether you made the wrong decision about moving away won’t affect whether or not it was, and so I would say that you should focus on what you can do now and in the future for her.
To build up your relationship, you will probably have to see her. Children that young aren’t really able to develop a relationship over the phone. Although, I would say that just because she won’t talk to you on the phone doesn’t mean she’s mad at you, or that even if she is that it’s irreversible. My children really disliked talking on the phone when they were that young, even with people they liked. It was rare that they would spend more than a minute on the phone.
If you go see your daughter, and then disappear for another 6 months, she won’t likely remember you, nor have the good feelings about you that it sounds like you would like her to have.
My best advice is move back. Should you decide not to, it will take a lot of effort on your part to be a father to her. Number one - no matter how much you may ever feel that you aren’t giving her enough, don’t walk out.
Regardless of whether you move back or not, most of the following would be good:
Continue to call her, and keep the conversations short. Send her pictures of you, maybe along with little gifts (don’t try to buy her love, of course). Do you and her mom both have computers? Buy webcams for both of you and spend a few minutes here and there, as often as she is comfortable with, interacting with her that way. Call her mom often to see what is going on with her. Did she learn all her colors this week, can she count to 20, etc. Celebrate her accomplishments with her, even if it’s only by telling her how proud and excited you are.
Speaking of her mother, make sure that she understands how important your daughter is to you, and what kinds of things you want to do to be part of your daughter’s life. She will need to understand that you are doing this because you think it’s best for your daughter, and that it’s not out of obligation, but love for her. Ask her mother what she thinks you can do to strengthen your relationship with her.
If you have family near her, ask them to visit with her occasionally. Have her mom get her to draw you pictures and send them to you. Then hang them on your fridge and other places, so that you will have constant reminders of what a wonderful little girl you have helped bring into this world.
Pray that God will help you keep your focus on your daughter, so that you will always continue to do what is best for her.
Thank you for wanting to stay in her life. I say that as a daughter whose daddy was gone most of her life, but always loved her. I also say that as a mother who is divorced from her boys’ father. It’s frustrating to be on any end of this, please don’t ever give up.