If it appears to be a jealousy thing, then she is probably acting out for attention. She has probably been getting less attention since your youngest was born (understandably), and is missing the 1:1 attention she used to get. She's obviously figured out that if she does the right thing, it doesn't get noticed much, but if she does the wrong thing, that gets noticed - and in her mind, negative attention is better than no attention at all.
With kids I work with who are misbehaving for attention, the key thing to do as some PPs have said, is to try to ignore/redirect the misbehaviour (as much as possible) and catch her being good. Then ham up the praise when she does something good, even if it's really small. Positive attention is much more desirable than negative attention, so if she knows a particular behaviour is likely to attract praise, it increases the likelihood of her doing it again. Or focus on one behaviour in particular with a rewards chart - but make sure she understands exactly what 'being kind', for example, actually entails - keeping her hands to herself, only saying nice things, sharing etc.
The other thing you could try is maybe spending some special mummy-daughter time together, just the two of you. Since your DH works, maybe on a weekend when he's home, leave him with the baby and do something special with your DD like go get a hot chocolate together, or take her to the park, or go to the movies. If she gets jealous of her brother, she will probably relish the opportunity to spend time with you 1:1, will behave better and you'll get to see that nice side of her again - and be reminded that she's not a terror all the time!
Good luck being a mum is a tough gig!