Im sorry to ask this but does she see anger or negitivity?
Maybe you or your partner react in an angry manner when you are upset or are negitive about things? Kids just mimic us really don't they?
Im not judging you. I have 2 and my eldest Dc can really get on my goat and last week, all week I felt like I didn't like him. I know what you mean, id just look at him and he'd annoy me.
I just thought that maybe if you understand where she is coming from you more you'd feel less irratated by her.
She probably picks up the vibes from you and this is why she acts up so much. (this is my theory on my DS anyway).
I agree with spending time alone with her doing nice things together.
It may take more than one outing if there is built up resentment there then chances are the first outing could end in disaster but presevere. You don't want her growing up feeling she was less loved than her younger sisters.
I hope this doesn't sound like im being horrible to you. Im honestly trying to be constructive. I feel for you because I know how it feels.
I took DS out on a picnic (without his sister) and we (eventually) had a lovely time. It reminded me of nicer times and his good side. It also broke the cycle of him acting up, me shouting, him acting up.
Good luck, hope you get somewhere with her.