If you possibly can, and I know it's difficult with a baby, make some real one on one time with her.
I had exactly the same situation as you, similar age gap and move, and the thing that really helped was giving my three year old some undivided attention, and letting him know that things could still be as they were before the baby and the move, even if only occasionally.
I took him to the cinema, but could be a quick trip to the playground, cafe for a treat, shop for a small toy etc, go round the block with her on her bike chatting. have fun with her and really listen to what she wants to do. On the floor, playing, undivided attention. Even just once a week made a huge difference.
I thought that it was enough to do this while the baby was asleep etc, but the key thing was us going out leaving the baby behind, and doing something just us, that seemed very important.
I breastfed so didn't have much time but managed to leave her with DH for the odd hour here and there, his behaviour improved so much once we did it, and now I just try and remember to top him up with some one on one time every so often.
The other thing is try not to give too much negative attention to the bad behaviour, just 'no please don't hit/tantrum' etc then turn away and be distracted by something else. Hth