Sending you compassion: you are in the centre of the storm, and it will soon pass.
From what you say, you don't actually hate motherhood at all - you just need a break. Somehow, we understand that carers of adults need respite, but think that rule doesn't apply to carers of (even needier) children.
I resolved my own case by going back to work. Yes, childcare cost my *entire* salary (not even exaggerating) but I regained my sanity.
We're in the middle of a pandemic, so you might have to cling on a little longer until you can get out of the house, so you might consider forming a 'bubble' with another family in your situation, and alternate the childcare. Anything that gives you the space you so clearly, desperately need.
In your shoes, I'd focus on just getting through each day as it comes. You've already said it is improving for you (good!) and it will continue to do so.
By the time your child is four, you'll barely remember how awful it was, and just enjoy your wonderful child. (Don't worry, she'll be just fine: she knows you love her, as you know in your heart that you do.)