OH GOODNESS! To hear you say you are almost giving up isn't good at all! That isn't what your daughter ever needs to hear or feel from you.
She is three, a time of strong wills, independence, confusion of growing up but wanting to be a baby too, inability to vocalize frustrations. She needs you to be there, she needs you to understand what is going on. Kids DO NOT wake up in the morning and decide to piss parents off. Behavior issues stem from hunger, not enough sleep, wrong nutritional intake, changes in the family (you just had a baby less then a year ago), to all sorts of reasons, but kids don't want to be bad or you to be angry.
I learned in therapy with my daughter that you CANNNOT control a child but you have to teach them to control themselves.
Does she make eye contact otherwise, if she is happy? Does she do the same things over and over again in play, does she socialize with other kids her age? Is she able to speak well?
My only concern would be having her evaluated for mild autism. I know that is a scary thought, but trying to determine if her behavior is typical three year old behavior or if something deeper is essential. Early intervention if it is something out of the norm can save her and you in the long run.
Both of my kids never had terrible twos, but lordy at three it was a nightmare. Even when my daughter turned five I finally had to call our Pediatrician to recommend a therapist, a play therapist because I was so beyond what to do with her and her bad behavior anymore. Finally we found a way to communicate, for me to understand her better, for me to lessen my stress and anger and us to work together. It was a long road but we got there. She had a lot of issues due to my divorce that I was so unaware of.
Consequences are essential, boundaries and establishing them are priority. You have to keep your cool, be consistent, be firm but loving. Sounds very hard but it can happen. I still lose my cool and AM NOT the perfect mom, but I know now to step back and figure out what is going on with my kids to understand how to get behavior back on track.
Maybe your daughter needs more one on one time with you or your hubby? I know my daughter adjusted to her brother coming when he was an infant but when he got mobile and more in need of eagle eyes is when it was hard for her to adjust to the lack of attention.
Find what works with her, losing a priveledge, losing dessert, taking a toy away,naps, something has to be important enough to bring the bargaining table. I would read as much as you can about autism though and if you have even the slightest concern, have her evaluated, you owe her that much.
Don't give up, we all have been there to one degree or the other. Nobody I know has perfectly well behaved children.
Try diet changes, more sleep, consequences to are working for you and all that. Just giving her a place to cool off and then go back and talk about what happened. Keeping them accountable for their actions is a tough lesson but so important.