You sound like a fab mum who is doing everything they possibly can but unfortunately not getting the results you would like.
It does sound a bit like your little girl may be used to ruling the roost a bit. She also sounds quite strong willed, having not read your previous posts I am sorry I don't know all the back ground info.
My little girl has always slept and eaten well (I know this doesn't help! Bear with me...) but she is strong willed and even now (she is 3) she still tries to get away with it. Whilst I do think we shouldn't try to quash her personality I do give her very firm boundaries of what is acceptable. We do joke that she is the diva in the house and she is dramatic and its her way or no way etc etc but if she starts to try and push it too much I nip it in the bud quickly and she soon learnt just how far she can push.
I'll try to give some examples -
She might request something food wise then when it's made she will wail that she doesn't want it. So I tell her in a calm but very firm tone that I made her exactly what she wanted, I am not making anything else so she eats that or has nothing. (I am not always this strict, just if she is having a moment!)
She'll throw herself down on the floor as though the world is coming to an end. I step over her (and sometimes hum a little tune to myself!) and ignore it and as soon as she shows signs of calming down I'll ask her if she wants a cuddle.
I feel a bit like I'm stating the obvious above but I have two boys who have never been anything like this and are placid and soft and easy going, my girl is a little madam!
When your DD cries at bath time I would talk to her in a fairly level tone about what I am doing (just rinsing your hair then we'll do your teeth) carry on regardless of her screams, don't try to console, I'm sure she'll learn that it has to happen and I find talking through what to expect always helps.
If she kicks off at meal times calmly get her out of her seat and move the food away. You will pick up any signs of her suddenly thinking actually I would like that and can react accordingly.
Do you have her in a really good routine? Like, pretty much to the minute? Just thinking if you've recently moved naps etc that might not be helping with the unsettledness. Make a plan and stick to it like clock work, I know how hard this is but I really believe in it and it has always worked with my 3, it's not forever, just whilst you're trying to establish what she should expect and when, once she's settled and you feel a bit more in control you can let it slip a little, at the end of the day you still have to get on with life.
Feel like I've rambled forever but can tell how distressed you are.
One last thing, and I am crap at this, when she has her big nap have a sleep, I know it's the only time you can get stuff done etc BUT that really doesn't matter AND again it's not forever, just whilst you're getting her sorted before your new baby comes and if you are rested then you will have so much more patience etc.
Good luck and let us know how it all goes.