Miss 3 has a major meltdown if I stir the porridge that I have made her or I put the sugar on wrong or if her brother strokes her hair. At this age they are trying to have some control over their lives and they just don't know how to negotiate. I guess your dd has the added issue of a new baby. I find it easier if I 'don't get sucked in'. If I view my dd's behaviour in the 3rd person, believe she will not be driving me batty for the next X amount of years and that this is just a phase. Maybe youtube some clips about development at this age- it kind of helps me feel a little sorry for my dd which lowers my levels of stress and anger.
Also I am not passing judgement on you but thought I would mention it. A mum I know is constantly telling her child off in a high pitch screechy voice. She picks him up on everything so it's constant yelling, telling off etc. Being at her house for an hour does my head in so I can only imagine how it is for her and her ds. I'm not sure if her parenting tactics are causing him to act out or if his antics are causing her to parent in that way. She asked me if I am always yelling at my kids and I said no. I did say that I don't pick my kids up on everything and if I do pick them up I try to 'redirect' rather than 'tell them off'. Hope you don't think I am being awful, just wanted to share that.