Edelweiss, my heart aches for you. I've followed this entire journey (or in the words of Mountain Ash, the whole story thus far) and know how much you love A. The mother is being selfish and ungrateful. Unfortunately, at the moment, she holds all the power, and because she does, I would echo AdornmentsMilani.

We had a similar situation here; years ago, DIL made it almost impossible for us to see our granddaughter. When it finally seemed that there was nothing left to lose, I wrote a letter to them, reminding them of how much we loved them, of what a good father hubby had been, how valuable extended family are in so many immeasurable ways and how children need as much love in their lives as possible. I poured my heart out, trying not to be condemning or judgmental, but gently reminding them that family and loving relationships are more important than whatever it was that was keeping us apart. Even I was surprised that it worked; hubby's son was on the phone that night. That was about six years ago, and while the road has been a minefield at times, our relationship with them and the grandchildren has blossomed to the point where I don't think they would use the children as emotional blackmail again.

I don't know what would work in your situation, but I echo everyone else's assurances that "this too shall pass" and hang in there, don't burn any bridges - you want to be there when they - more specifically, A - need you again.
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When you don't like a thing, change it.
If you can't change it, change the way you think about it.

(Maya Angelou)