Has your DP tried replying (when she says she doesn't like him), "that's such a shame, because I love you very much". He needs to keep acting like he always has done, and she'll see nothing is changing.
Saying "I don't like you" in response to being told off/asked to do something she doesn't want to do is normal 4 year old behaviour. A 4 year old can't articulate further than that. I remember my 5 year old saying to his friends, "if you don't do x, I won't be your friend" - kind of similar. It's a childish way of taking a stand, before they've learnt any real negotiation skills.
I also think you are putting ideas in her head, asking her if she's jealous. You're putting adult perceptions onto a 4 year old, who probably hadn't considered the new baby as anything other than a bump at the moment. Concentrate on involving her - getting her to listen to the bump, feel the bump, encourage her to love the baby, not fear it.
My own DCs have been known to tell me they hate me if I make them do a chore. They don't mean it. When I say what a shame that is, as I love them very much, they look a bit taken aback.
AGree with christinarossetti too - start to articulate with her, "you sound very sad", "you sound very angry" - sometimes just having your feelings acknowledged is enough. If you just tell her not to be "nasty", that's telling her that SHE is bad, and she'll probably feel even more angry or sad, because she'll think YOU don't like HER!