I can relate to you, I have a horrible relationship with my grandmother. (It sounds just like her situation) I don't mean to be the bearer of bad news, but you did ask for opinions (please do not take this the wrong way) She is not only your daughter but your husbands as well. The only person you would be "punishing" by not letting your MIL be a part of your daughter life is your daughter. You certainly do not want your daughter growing up and resenting you because you deprived her of seeing her grandmother, do you? On the other hand I can see how you do not want her to deal with the drama. At her age there is no way that she could know what a pain your MIL is being or how her actions are wrong, all she knows is that people love her. A baby can never have to much love! If your MIL is as bad as she sounds, which I am sure she is if and your husband were upset, then your daughter will grow up to realize that herself. This will make your daughter realize that your MIL is not a good person by your MIL actions, not your or by hearing you/your express your opinions. Obviously if she is verbally abusing, speaking badly about you or your husband, or physically abusing your daughter than I would not let her see her but I feel like you need to give her an opportunity to see her grandchild.
My MIL can be a nightmare at times but one thing I have learned is that if I speak badly about her my husband is in the middle and makes him feel uncomfortable. I do not want my husband to resent me for feeling badly about his mother, so at time I just take what she says with a grain of salt. What I have come to realize is that people are they way that they are and there is nothing that I can do/say to change them, so I cannot worry about them only myself and my family. What I am saying is let your MIL weed herself out of the family, don't take it into your hands, it will only cause conflict with your hubby and your daughter later in life.