BallroomGranny, apart from sending M the exact story you have posted here, there is nothing you can do.
I get the feeling you live in the USA - probably in a small town, but that is neither here nor there, except that it perhaps explains some of your to me hidebound attitudes and old-fashioned opinions.
M is a single mother and thus the sole guardian of her child. She, and she alone, has the right to say who she and the child will associate with.
On your own admission you have said some very nasty things to her, so it is hardly surprising that she does not want to see or hear from you.
I realise that you were devastated by your son's death, but that, as you have come to realise, does not excuse your behaviour.
Grandparents do not have any real rights to see or know their grandchildren, especially when the child's parents were not married, nor apparently, intending to marry.
All you can do is to hope that M might one day get in touch, although in her place I would most certainly not do so.
You could of course leave money in your will to your grandson, if you are now satisfied that he is your son's child.
One little ray of hope is that the child may. when he is older, want to know something of his father's family and contact you himself. It is unlikely, given what he will have heard about you from his mother, but it could happen.
Try to concentrate on your daughters and their children and on a life that does not entirely revolve about family as well, instead of repining over something that probably cannot be mended.