I'm a little confused by your post, mostly a little confused about the spoiled princess label.
I think I would more describe your daughter as physically abusive to her smaller sibling, sexually inappropriate with peers at school.
Reading your post it sounds like you have a blended family - could she be acting out because of that dynamic, or is it possible she's been sexually abused?
Best wishes.
my heart goes out to you ,, and your daughter and family all siblings argue ,, but i also feel shes crying out for help ,, dont automatic thinks shes like her dad ,, but she would need to me accessed ,, id rethink how you correct her also ,, shes needs love praise and understanding ,, and yes correction ,, suitably for a seven year old ,, i would stop spanking etc,, as your inpounnding this behaviour ,,