McBlubber, I could have written your post.
All I can say is that I was following a negative script handed down to me by my toxic mother, who I now realise is the most negative, cruel, self serving narc you will ever meet.
I did not want to be like her, and it was quite a shock to realise I was. Exactly like her.
So....your statement "I tell her I love her and give her cuddles but I do not like her." - yes, I know exactly what you mean. And I think you are very brave to admit it to yourself.
And on a deep level, she knows it too, which is why she pushes you so hard.
I think its a case of "Fake it till you make it".
There is no easy fix to this, but to start with, start to be OTT positive about the good. "Ah I love it when you are so kind to your sister/cousin/friend/Cat" and other positive statements that will ensure that she knows you care about her... And you do. You dislike the behaviour, not the child, and I think you have to accept and internalise that fact. You love the kid, you hate the behaviour.
Follow up with a small reward on the good days and give positive affirmation about how much you enjoyed your day/morning/visit with her. Dont be tempted to add the negative "because you behaved yourself for once!"
Also, when she has done something wrong, do not resort to negative statements about her - make sure you focus the negative about the behaviour. So eg dont say "You are so naughty! Why dont you listen!" rather say "I feel cross when you don't do what I asked you" and "I dont like it when you hit your brother, it makes him sad and it makes me sad".
I found also that my DD had to learn to name these crazy emotions, and be able to vocalise "I am feeling grumpy!" rather than lashing out. Sometimes its important to stop and acknowledge the emotion, rather than focussing on the behaviour, eg "I know you feel very cross when your brother takes your barbie doll, because its your precious thing. But I feel sad when you hurt him, and I would like you to be kind to him instead."
Try offer sanctions as a choice..."you can stop tormenting your brother or you can have early bedtime this week - which would you like?"
or
"You can put away your dollies, or you can lose your bedtime story tonight, which would you prefer?"
Find a sanction that she will care about. ALternatively find something that she really wants to do. One of mine was that if she behaved, she could have a bath with her socks on. The novelty worked, once.
Look at reward jars/sticker charts.
Try to target a specific behaviour rather that generic compliance and global good behaviour - Thats unrealistic. Pick one specific behaviour you would like to change, and set a target that could be met in a week with effort. Reward with a low cost treat - a comic, a trip to the park or pool, staying up 30 minutes later.
Be generous with your stars and stickers. So if the target behaviour is to be kind to her sibling, then any act of kindness gets a reward, bad behaviour doesnt get a reward, or necessarily a sanction (depending on what you target) but certainly you would comment "What a shame you thumped your brother, you could have had another 3 stars on your "going to the swimming pool with the slides" chart.
Dont stop trying to bridge the gap between you - it may take time, but you can do it.