"dd2 is … well, it doesn’t matter how much love and attention she gets, she just obsessively targets dd1, who can’t have anything at all because dd2 just takes it off her and screams"
I was once that DD1, OP. My sister was a little shit. I was always very careful with stuff, I could play with my auntie's ceramic animal collection and would not break a single one of them. I followed the rules. I was quiet. My little sister hated me. She would wait until I would finish a clay vase which had taken me all day to make, and she would sneak into my room and smash it, and smile when mum was not looking. She would draw doodles in my favourite books, and pull the pages off them. She would come behind me and pull my hair, really hard. She would hide my glasses so I couldn't see and my mum told me off for losing them.
My parents said that she was just small and I was the older one and had to put up with it.
One day I exploded. I don't even remember exactly what she did, but we were home alone while mum and dad had gone somewhere (we were children of the 80s, were left home alone a lot), and she did another of her cruel things to me. And I just lost it. I went into a rage, accummulated after all those months and years of holding it inside. I beat her up quite badly, pulled her hair, pushed her, threw her around... to the point that, when I came back to my senses, I was holding her by the neck and starting to squeeze. I stopped then.
She of course waited until mum and dad got back and started crying and screaming as soon as they came through the door. I admitted everything, and said "and I will do it again if she ever hurts me or breaks another one of my things". I got punished for hitting her. But I didn't care.
You know what? The little shit never, ever came for me again.
Even the mildest of children has their limits, OP. If you don't protect your DD1 from your DD2, DD1 will one day explode. And it will be ugly.