Hi! I'll be glad to help you with this issue.
First, let me say I can imagine how distressing this situation must be for you. It must not only be frustrating for her mom because she doesn't know what to do to help and nothing seems to help, but it must also be heartbreaking to have your little granddaughter so distraught. This is not an uncommon problem at your daughter's age because bonding is such an important developmental part of being three. This is an age where there are so many developmental leaps and surges happening that anxiety is very prevalent.
There are no books for the general public that I can recommend; the books for therapists are also way too detailed in their theoretical foundations to be readable for people. However, I'd like to offer a strategy that has worked in my private practice; the strategy is on behavioral therapy approaches founded in attachment theory.
You say that the father is more or less around in her life, meaning that he's not totally absent. Good. We need his help in this. At least via Skype if nothing else.
There needs to be something of his that she can associate of his, a sweatshirt or a handkerchief, or something similar, okay? If he can be convinced to come around a couple of times to establish this connection between the object and himself, even better. If not, then something that's left where she's living that was his will be second best. He would need to have a similar handkerchief or other object with him to show her via Skype. If not, then buying two handkerchiefs, etc. with her holding one and him the other via Skype is the best we can do, so that's what will have to suffice.
I'll address this to him as he needs to play act this, so he needs to read it:
The procedure is that you tell her how much you love her, how she's your precious one. You repeat it. You then tell her that it's not the time for you to be there with her right now, but that doesn't mean you don't love her. And you want her to know how close you are to her so here's the sweatshirt/handkerchief that you want her to have next to her that will comfort her and help her know that she's safe. That she's loved. You repeat this whole speech. Very childish language. Speak in sweet, childish ways about how this handkerchief or shirt is like your love for her and like how good everything is.
And you kiss the object and you give it to her and hug her. Then you tell her how when she has the cloth, it's like you're with her. You do this a few times, letting her know how that when she has the handkerchief, she can feel good that it's like you are there with her, your love is there with her. Do this a few times.
Okay. Now, her mom needs to take care of this cloth and have it accessible for when this occurs to be able to remind her of how daddy's love is there with her. And she keeps reminding her of it. The key is repetition. Both by the father and the mother. The mother is key here as well, because she has to keep repeating that the handkerchief is daddy's love being there with her. Because the daughter may take a while to test if mommy really means it.
Okay, I wish you the very best!
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