Your daughter, from your post, sounds immature and flaky, to be honest.
Using your GS, as some sort of bargaining chip, and holding him over you as a threat, is not the action of a loving parent.
If she thinks you were that awful, why on earth has she allowed you so much unsupervised contact previously?
It doesn't make sense. Surely, any AC that really felt they had awful or abusive parents would keep their children well away?
All you can do, at the moment, is to be a lovely granny when you do see him. Give him fun days, don't talk about his mother, and he will form his relationship with you from that.
Hopefully, one day, your daughter will grow up a bit, and if she's got an issue with you, then talk about it with you.
These ACs that use their own children like this, to get at their parents, really aren't putting their children's needs first.