I think you are not seeing the real issue here. The post seems at first to be about grandchildren and favoritism, then you bury the vital clue: She says she despises you and your husband. I can't imagine that her despising you is only about the step-grandkids, is it? There is clearly a LOT more going on here and it's the fact she did not want you to marry your husband and she despises...him, and your marriage. The kids are just part of that whole package. I would not even think about working on her to be more fair to these kids until she can come to terms with the much, much larger issue of her learning to accept your marriage and husband.
It sounds as if she is, perhaps unconsciously (so she would deny this if you asked), expecting your marriage to end. Or she's just ignoring your marriage. She is acting as if you and your biological daughter are the only people with whom she has to be concerned, and that indicates that she may be feeling that if she just pretends you don't have other family members, then they don't really exist. Not to her, certainly.
So deal with the real issue here -- her dislike of, even her emotional denial of, your marriage and your relationship with a man of whom she disapproves.
If you just push the issue of the grandkids, honestly, you're letting the bigger issue slide.
The best thing you can do to make her see that you are all one family unit is to go on acting like one-- doing things together, presenting a united front, treating all the kids equally yourselves. And it sounds like acting like the family you are is the only way you'll ever make your point, since you are not speaking to her.
One other thought: I am NOT saying this to let her off the hook, but....You also can't expect anyone to be a perfectly fair grandparent when the situation brings not just a few but four new children into her life instantly. Just saying "these are grandchildren now, treat them exactly like the child you have known since birth" is really expecting too much, too fast. Yes, she should make at least a surface effort to be fair with gifts etc., but after all -- she has indeed known your biological child since birth and does feel closer to her. Add that to the mix of your high expectations, and the fact she is in denial about your marriage lasting and being "real" to her, and she's going to favor your child. But if you and she are not speaking -- how exactly do you ever plan to work on this?
I'd go back to talking to her, say you want to start over, say you DO realize that it must be tough on her to have four new grandkids materialize all at once (in other words -- be a little emphathetic and say you see that it's hard on her) and then remind her kindly that the kids themselves did not make their situation and that their dad has rescued them from a bad biological mom. Suggest that if she can't quite think of them as "grandkids" yet that she think of them as decent kids caught in a bad situation, and to treat them with the kindness and decency you know she is capable of showing (even if you are too mad to believe that right now, SAY it). Give her the out of saying you know she needs time (three years of your marriage is actually not long over a lifetime of grandparent-grandchild relationships) and then find ways for her to get to know these step-grandkids. Invite her to their school events, their sports events, etc. Do not press her to spend gobs of unstructured hang-out time with them where she feels she has to entertain them. Help her get to know them.