He only gets to make the full decision for himself, this child has two parents who get to both make decisions for that child
But the decision for the daughter to have contact with the DH's mother lies with the DH, it is NOT up to the wife (the OP) to take it upon herself to take their child to his mother, when he has specifically said NO. (And that he does not want her in their lives.) It HAS to be a joint decision.
No matter how much the OP cries and moans, if her DH says he wants his mother to have nothing to do with his child(ren,) then his wife (the OP) must respect that.
But his mother isn't very abusive. If she was then I wouldn't even dream of having this conversation. It's not me I'm thinking about it's my daughter. Why are people finding that so difficult to understand?
Makes no odds that his mother is not abusive 'nicegurl.'. He wants nothing to do with her because of what she did in the past, and he wants his child(ren) to have nothing to do with her either. It's not your place to take the child to his mother's against his wishes.
Why are you being like this? Why are you not taking your husband's feelings and wishes into consideration? If my DH behaved like this, I would be re-evaluating our relationship. And if he did (to me) what you are planning to do, it would seriously put the marriage in jeopardy. If he has that little respect for me, he would not deserve to be married to me.
What people are finding hard to understand is why you are being so stubborn and pig-headed, and are refusing to listen to sensible and constructive advice! As I said, you go and do what you want then, and we will see you on MN in a few months when your DH has left you for being so horribly disrespectful, not listening to him, upsetting him, and causing him pain and hurt, because you just HAD to have your own way.