You have put your Son and the rest of your family in a very difficult position, Hope, by wading in and trying very hard to fix something which was not really your place to fix. I hope I can say that to you, because that's probably what I would have done - ever hopeful and trying so hard to imagine that eventually some good would come out of a bad thing and a reasonable solution would bring about some happiness for all. Not the thing to do, though, however good your/my intentions! If it was a mess, it was down to him and the mother of his child to resolve it between themselves, however much you may have liked the idea of helping and becoming a Granny.
Where you ended the first paragraph of your post, that's probably where things should have stopped. Your Son has made it clear - presumably long before the child was born - that he wanted no part in fatherhood and if the baby's mother went ahead with her plan to be a mother, that was a decision she would be making on her own. She was clearly determined to keep the child. Good for her for being responsible. However, she's never thought this through properly : she's clearly determined that your family, you and the baby's father must be involved - otherwise the child will be "damaged". She has treated you all to some unpleasant 'phone calls and because you were worried about the pressure on your Son, you intervened and have seen the child on her terms. You can see now that this is not good enough for her - she wants more. Your own family can see however that they are going to step into something very challenging without your Son being involved; it's his business so they respect that and are staying away. It would appear that the Mother cannot accept that your Son will only contribute financially to his unplanned child's upbringing, she continues to have some "dream" of how she would like her baby's upbringing to unfold, irrespective of the realities and the wishes of anyone else involved.
I think you should sit down and explain that requests or demands for love and interest cannot be forced upon anyone. You have no control over your Son or your family, any more than she has, so she honestly needs to accept that as things stand at the moment, there's only you there for her and the baby and if she continues to make things very difficult and uncomfortable for you, then it may be better for everyone if you back off a little until she is more accepting of what might be achievable. She's not being realistic and she is going to get nowhere by putting pressure on your Son or you and the rest of the family. If she doesn't accept this, then you will at least feel you have spoken and done your best. Trying to co-erce your Son, maybe demanding meetings, access, counselling, etc., etc., will be a road that she should avoid. Accepting the situation and not thinking that she can change it, but being reasonable and looking towards her own and her little boy's future would be a much more sensible path for her to follow now.
Best of luck with it all.