OP, I think you are trying to hard to try to explain why she behave the way she does and by doing so, you are at risk of associating her with problems that don't exist.
Some kids welcome change with open arms, some hate it. Some older kids think that the arrival of a sibling is the best thing in the world, others wish they could kill the baby. I expect your SD just fall under the second category, but it doesn't mean she has attachment issues, or isn't being disciplined appropriately, she is just a bit more emotionally vulnerable than the average child.
My view is that the worse thing you can do is reinforcing the issue by keeping them apart and making a point that this is because she is nasty. That will only tell her that she is right to be concerned and make her react even more negatively. Instead, you and her dad need to make her realise that not only it isn't impacting on her relationship with her dad, but that actually having another sibling, even better of the same age, can be great fun. Make a genuine effort not to compare them, even if you think you are hiding your thoughts, if she is an emotional child, she is more likely very perceptive too and will pick up very easily that you (and maybe her dad) think that your DD is better than her, maybe prettier, more intelligent, more lovable, more worthy of affection.
I would really encourage to do as much things all together and treat the girls exactly the same way. Plan fun events so that she can learn to associate pleasurable time with being with your DD. Take both of them shopping and buy her what they want. Emphasize how they are both beautiful in their own way, that their individual tastes are both great and suit both of them. If you DD finds school easier, think of something your DS is quicker to learn and point out that everyone has different skills and that what matters is trying their best all the time etc...
It will take time without a doubt, but you can definitely make it successful if you can genuinely find it in you to care for this girl and believe that she can turn into a lovely person too.