Some very good advice here.
Just wanted to add that if I had a penny for every thread I read on Mnsnet about difficult behaviour in 4 yr olds then I would be v. rich indeed by now!! People talk about the terrible twos and the challenging threes but for some of us, it was definitely the 'fours' that were most difficult. It's a time when many children try and test limits.
It's doubly difficult if your child is bright and precocious so I agree with the others and your dh, that you are being v. hard on yourself.
I recognise quite a lot of what you are saying as I have quite a demanding dd and she is an only child too (and I tend to dwell on negatives!!).
The fact that she is an only child makes for quite an "intense" relationship between the two of you, which can be draining in itself. I thought I would love being a sahm too, but once dd reached 3.5 yrs I was climbing the walls and our relationship is much better now I work p/t because I am happier in myself....
You may find that her behaviour improves quite a bit once she starts school. She may be a bit more demanding initially because of the change of routine and because she will be tired etc, but you may find that the structure, and different activities and friends that she will encounter at school will give her the outlet she needs, particularly if she is very bright.
Oh and have just remembered (although this may not be at all relevant in your circumstance - just mentioning it in case useful) that the times when dd became most 'ready to combust' were, looking back, when she was on the brink of a 'developmental leap forward' and/or I was unknowingly/unintentionally holding her back in some way by still doing things the way I had done them 6 mths before, without realising that she had moved on (if that makes sense).
If she your dd is very angry (the clawing behaviour etc) perhaps this is her way of expressing that she needs more control in her life? Anger is usually a cover for frustration. Before she starts school, could you possibly give her more control over "the little things" such as a choice of appropriate clothing or a choice of food perhaps? That definitely helped calm my dd down a little.
If you are doing this already, maybe she just needs a different way to express her frustration, through drawing or role-play etc. I tried all those things with dd (we even had 'traffic light cards' at one point so she could tell me if she was just irritated, or angry, or VERY angry!!) and she's a lot calmer now (although that might just be because she is older (6 yrs). Tbh, she still has her moments and I am still quite 'shouty' but it is getting better!
Finally, yare not alone. I think EVERYONE finds parenting very, very hard; because it is!!!
And although it is a definite milestone ... she'll need you even more once she has started school I promise, so don't for a minute feel "all is lost"!!
Good luck with it!