As a teacher myself, it is imperative that you stick to your guns! I can not tell you how detrimental it will be to your daughter to push her into a grade she is not ready for! It is far more destructive to passs a student who isn't ready than it is to hold them back! And, I'm speaking as a teacher, here. I am appalled that her school is trying to push her through!
As a parent of twins, it is very hard! Our boys are only 4, but we already notice a big difference developmentally between the two. And, yes, it is very important to treat them as individuals instead of a package. My sister (not a twin) was held back in first grade and was never teased for it, although she was the oldest in her class. Had she been forced to proceed while not ready, she would never be where she is today.
Whatever your decision, remember to do what is best for your daughter, regardless of her twin. What would you do if she was not a twin? If she is pushed through with her sister, it's only going to make her feel like more of a package deal, IMO. Let her progress at her own pace and she's likely to be happier about her own life, rather than feeling second rate to her sister.