Although my DS is an only I can see that he is as many of you describe; he is totally his own person, incredibly strong likes and dislikes, his own opinions, doesn't have a 'wanting to please' cell in his body, is also very independent in some ways but clingy as well......
I can see that if he had come along as a second child, after a compliant and biddable first child, I would be totally floored.
So I do sympathise.
I think you do need a break from her - remember how you feel now, when the time comes to leave her in Sept at Nursery - and just go even if she has to be peeled off! She WILL appreciate you more for having had time away from you.
I also firmly believe that she is going to have absorbed some of your stress of the last few months and this will be making her harder to deal with.
It's unbelievably easy to get drawn into a negative cycle with kids like this and I agree with others who say ACT as if you are besotted with her, as if everything she does is adorable....if she is getting impossible, laugh and smile affectionately and say "oh, I do love you, you're so gorgeous" when you are thinking the opposite! It's got to be worth a try.
Toddler taming is brilliant, read if you haven't and give it another look if already familiar.
and accpetance is a wonderful thing - she is as she is and whether you give yourself a stroke getting angry about it, or let it wash over you, will not change her!
I do really really sympathise, hope things get better.