You're not doing anything wrong this is just DD1's way of adjusting to the new family dynamics and finding where she stands. Unfortunately sometimes the only way to cure this is time because it can be a crappy catch 22 situation - DD1 hits her sister, then you give her attention - either by chastising her or distracting her and then that makes her think, 'Oh, mum will give me attention if I do xyz, so I'll just keep on doing it' and when you've tried ignoring her, she gets worse because it doesn't get the desired result for her, ie Mum giving her attention. And TBH, in my experience I don't think it matters if your child has never seen or experienced a smack or being hit, it is just something that they will do - I know it is a common problem with AP families too and I think it's instinctual, and because it's mostly young kids/toddlers that do it, they can't verbalise how they are feeling so they lash out physically.

I would keep up the positive reinforcement when she does something nice to DD2 or to you and try to spend as much time with her on her own as you can - which I know can be really hard sometimes if you are having a full on day with bubs. But it gives them some reassurance that yes, you still have time for them. It helps make them feel secure in their place within the family. Sometimes I would even make sure that I had gotten the older kids a snack/lunch/dinner before I tended to the baby's needs so they saw themselves coming 'first' instead of 'second' to the baby ITMS? And remember that this too shall pass