We bought one of those small trampolines for DS when he was about 18 months old. The ones with the surround b.c he loved to jump at gymbaroo and in his cot. He LOVED it. Not sure if your DD would be interested, but it does give them a space to burn some energy.

My obs told me this one: she has 3 kids and when she had the third bub, she had a felt board on the wall and different activities and her middle child could choose 2 pictures of what he wanted to do while she fed bubs. It gave the older child some control over what they wanted to do and a bit of structure. She used to mix the activities/pictures, so there would be a picture of a train, or building blocks, or play dough etc. Bit difficult if your DD won't play independently - I think that's a first child thing b.c our DS1 and every other first child I know seems to want more interaction from adults and siblings when they play.

Also, when I came home with our third bub this year, I made a point of spending special one on one time with the older boys while DD slept. As much as the washing needing to be done or the dishes etc, we would sit on the floor and do a puzzle or get the paints out or bake a cake together. Although, my boys are older than your DD and I haven't had any jealousy issues with them. I think 3 is easier than 2, b.c they older ones have somebody else to play with, whereas, your DD is wanting just your attention right now.

The doll suggestion could work - especially if you praise her for being gentle with 'her baby' and make a big deal out of being really careful etc.
Lastly, you could try a playpen for your DS when he's on the floor so that he's not at risk of being sat on/scratched or bitten, especially if you have to use the toilet or grab the phone etc. I know you want to work on DD's behaviour so that she doesn't do this, but it could keep DS out of harm's way while you're working on it.