Sounds like you all could benefit from a good family counselor. You don't know whats going on inside her head and she won't tell you. Maybe she'll tell someone else. And maybe that person can relate on an adult level what's going to you in a way that you can understand. Then, maybe that person can teach the two of you how to communicate with one another - and her with others including her siblings. She may have middle child syndrome, feel like older brother is loved bc he's older and an only boy, and younger sister is loved bc she's "better" since you seem to receive love through touch - cuddling and snuggling - and that has led to the strong bond bw you and the other daughter. She may be very resentful and feel completely out of place within her family, which would create alot of anger.
I strongly suggest finding a good Christian family counselor who can help yall understand one another. Also, give The Five Love Languages of Children by Chapman and Campbell a read. It may help tremendously. You've stated that you've tried two of the five - quality time and touch (which she doesn't like). She may well receive love as words of affirmation, gifts, or acts of service. It sounds as if she's not receiving love at home, even though you try to communicate it to her - you guys may not be speaking the same language! And if her love language is words of affirmation, it may well be the reason she does so well at school (where that is piled on) and not at home.
I hated to be touched too growing up - but I was all sorts of allergy meds from the time I was 5 and they just make one REALLY sensitive to sensory input. My love language is gifts. As a child, typically the only time you see a gift is a birthday or Christmas (as long you have parents with boundaries, right?). For the child with gifts as a love language, they will starve on that frequency.
read the book and try the suggestions....and see a family counselor who knows what they're doing :)