Hi D.:
No one thinks this is out of the ordinary? - A beautiful child displaying constant anger to everyone around her and isolating herself from everyone.
Get a new pediatrician. If you need one, ask online here.
Spend some one on one time with your daughter every day - even if it is hard at first.
Talk to her dad and siblings and let them know not to give up on her. Like if she says "I hate you", it is hard but they could say, "I love you anyway".
Encourage her to do better. When she does, give her a giant hug.
I recommend no physical discipline - just time outs and removal of privileges but this is where the advice of a GOOD pediatrician comes in. The doctor can make recommendations to you on this situation.
If you don't like the answers from the pediatrician you are seeing, go to another.
Do you go to church? Is it something you would consider doing as a family or perhaps just you and your daughter?
Is she being bullied at school? Would she tell you?
If she is being 'exploited' by someone she knows, most children don't talk right away. That is when good communication comes into play because when she is ready, you will be there.
This is the hardest for me to say. If my hubby said to me that he "ever" gives up on any of his children, I will have a serious heart to heart with him. I hope your daughter has not picked up on your hub's feelings/behavior toward her.
Your hub needs to understand that it is the "behavior" and not his good little girl and he is the adult and needs to be able to separate the two. Maybe he could spend a little time w/ her daily too like take her out for ice cream or a walk at a pretty park with the spring flowers.
Little girls are happy and playful. Her behavior is not normal and it is your job as her mom to get to the bottom of it no matter what it takes. Don't give up and remember that you need support too, starting with your hubby to back you up 100% on this. This is when you two pull together - for your sake and hers. Stand united and persevere.