Poor mothering is a huge cross to bear, and your mother seems to have all the necessary qualifications for a medal in that regard!
There is absolutely no reason whatsoever why this lady should have any involvement in your pregnancy, the birth, or the upbringing of your child. Your pregnancy, your child, so you call the shots. If you do not want this pernicious influence over your child, you need to start getting tough right now!
I had a difficult mother - nothing so overt as your experiences, but I was an unwanted pregnancy and it greatly influenced how I was treated; and she was a lady with both severe PMT and a huge chip on her shoulder about being a woman and was perpetually locked in mortal combat with my Dad which led to some very difficult times for me and my siblings. But, bizarrely, she turned out to be a very good grandma! - so you cannot tell how things might go.
But, if she turns out to be a bad grandma, then you are fully justified in keeping her away from your child, whose protection needs to be your number one priority.
Poor mothering is not your fault and you are to be congratulated on all your achievements. Nor is it learned or hereditary - do not for one moment fear that you will also be bad at mothering - I had a troublesome mother, but my children seem to have turned out fine - I made mistakes, as we all do, but they are lovely people and I am very proud of them.
Good luck with this pregnancy - goodness me, it has ben hard won.