OP I don't know if you're still reading, but I wanted to add that while you did get a lot of great advice in this discussion, your posts make me think you may be *so* overwhelmed that you're not even sure where to start with some of it.
For that reason, I think there is nothing at all wrong with talking to a counselor. It can be something you just do a few times and then you're done... or if you like it and it works for you, keep going.
But sometimes even really basic advice is hard to follow if you feel totally and completely stuck.
I also wanna say that not only is your 4 yo's behavior sounding very typically 4 yr old, it's also very typical of a child with a new sibling. 4 yrs old is old enough to be able to have something of a conversation with her, asking her what she needs, asking her to talk instead of just breaking down into a tantrum... have you tried those things? Sometimes when older sibs feel threatened and less loved because of a new sibling, they will do WHATEVER it takes to get more attention from parents - even if it's negative attention. I'm just worried that if you stay in the stuck/shut down place you're sinking into, you'll be reinforcing this dynamic instead of helping both ofyou get out of it.
Many have suggested sitting on the floor with her, talking to her. I'd also add some time that is JUST for you and her. You said your husband takes her out so you can just be with the baby... well as much as you're not liking her right now and probably don't want to do it, you should see what happens in your dynamic with her if you say "You know what, I miss spending time with you when everything's good and happy and you're not upset. Once in awhile let's have mommy/daughter time just you and me. We can probably only figure it out once in awhile... but we'll start this weekend. What would you like to do for an hour or two with me?"
Seriously, this could have a HUGE impact on your dynamic with her.
Best of luck momma, what you feel is totally normal, but it's a dynamic that can definitely get worse and have a snowball effect, where how you feel and how you then treat your daughter impact her behavior and make her even MORE someone you're not liking much right now... which then makes you withdraw even more, etc etc. It could go to a very bad place... so try to find some support to try out new ways of dealing with her and see if you and your DH can shift this dynamic.
Good luck!