Rhubarbginisnotasin "OP, I understand how you feel but your dads partner isn't going to be going away anytime soon and I think if you make your father chose between you by using your baby as some kind of bargaining tool you're going to end up without your dad. "
The OP is not making her dad choose between her and his partner. She is making it clear she does not want to see her dad's partner. He can still be with his partner and see his daughter and grandchild. What he cannot do is force his partner onto his daughter as 'grandma' because that is not what his daughter wants.
"... what you have to put up with in order to have your dad in your life and the wee ones life."
I'm not sure the OP should have to 'put up with' anything to have her dad in her life and I cannot see what benefit this granddad would be to his grandchild. He let his daughter down, not sure I'd be overly keen to let him do the same for my child. But it is the OP's choice, of course.
And the OP is not using her baby as weapon, how very offensive, it is simply a case of protecting her child in a way her dad failed to protect her.
The only thing you have said I can agree with is that the OP has been hurt and I do think some counselling could help her to heal.
Nut I am not sure what evidence you have this person will love the child and "...what's the harm in your kid having a gran who loves it?" I think there can be a lot of harm having a toxic person in your life.
Blonde "...has the right of being nanny..." actually grandparents don't have rights over children. If the OP felt this person would be a good person to be in her child's life I am sure she could come up with a name for her to use. But it seems clear she doesn't want this person in her child's life. Why is that so hard to understand? Her opening post says "...telling my dad we wouldn't go anymore because of her nasty controlling behaviour and toxic attitude, she did various things which imo were bullying."
Nuttynoo "My gran used to get beaten by her stepmum, burned, had a marriage arranged at 16, but stepgran still adored my dad to the point of spoiling." I think you have a very, very warped idea about what is acceptable. Anyone who does those things should not be welcomed into a baby/child's life.
"... you would have ruined a relationship before it even has a chance." I think that is called protecting a child!