Huge empathy for you here - you are describing life with my DD when she was a similar age, I also had a tiny baby. 3 years on and I'm afraid to say life is still tough but it has got better. My DD now has a diagnosis of ASD and ODD, as well as being gifted, but the diagnosis hasnt changed the behaviour or the fact that it is exhausting to deal with.
We have changed our expectations of DD but she by no means has life easy (in fact, life has only got better since we've laid down boundaries of steel!). We discovered that she couldn't understand the idea of 'chances' - if she could get away with doing something twice, then why not 5,6 or 100 times? - so now she doesn't get chances, which sounds draconian, but makes her feel a lot more sure of where the boundaries are. Everything is very scaffolded for her - only one instruction at a time, a visual chart of what she needs to do every morning, warnings before a change of activity ...
We totally ignore screaming, just repeat ad nauseum what we want her to do "DD put your shoes on" ...(count to 10) "DD put your shoes on" ... "shoes" ... "shoes" ... "shoes" and get on with other stuff acting totally unconcerned but firm. The response time has got quicker and quicker because she knows we won't shut up until she does it (not getting angry is key for us as otherwise it feels like she just feeds off the negative attention).
If I want to hurry things up I do just walk out the front door on a school morning - she hates the idea of being left and will pretty quickly be with me (if she's forgotten stuff, then tough).
DD2 is 3 now and has survived being woken from so many naps I lost count (more sleep also helps in the coping!). Haven't found a solution to the obsessions, or the not liking her very much quite a lot some of the time, although that has improved as the behaviour improved.