My own personal experience is with my father. I've not spoken to him or seen him for over 8 years now. Long story but he had my entire childhood and beyond to sort it out and didn't. I've never had an apology and in the end felt I really didn't need or want him in my life. My mother remarried a number of years ago and her husband, my stepfather is a truly wonderful man and never had kids of his own. I want him to be our child's grandfather, not my own father. He is over the moon and so thrilled its unreal
My mother is very happy about this decision also I can tell you.
I have a wonderful half sister I am in touch with and her son, my nephew. And a half brother, although I don't know him so well as he is 12 years younger than me. Both from my fathers second marriage.
I am expecting my first child in May. I long ago decided my father would play no part in my childs life at all. He does not even know I am expecting. Or that I got married last year. None of it. My sister won't tell him, he doesn't ask about me anymore.
I don't feel for one second our child will be missing out by not knowing a blood grandparent. OK, s/he will have my step father, so it slightly changes things, but I'm happy with the choice, my hubby supports me in it and our child will be shown much love by those who do play a part in his/her life. I'd rather that than suffer my father playing a part when he really has done nothing to make me think he a) deserves to or b) wants to.
I think you should really consider if you feel your child will be missing out? And if your mother is going to continue to be awkward, mean or whatever, should you inflict that on your child? If it were me, I'd say no. You've opened the door, so long as you leave it open, send cards on birthdays etc its up to her to make the effort then. Your son has people around him who love him
A Granny would be lovely, but only is she is going to be a proper Granny and embrace the whole picture, not just a part of it.