It sounds to me like she is in desperate need of attention. Maybe she is feeling left out? Perhaps some one-on-one time with her during the day will help. Maybe spend an hour painting, drawing, cut and pasting or take her to the park.
Kids usually act up when they want attention - any kind of attention is better than none. When i was little I was such a terror, my mother told me i used to tell her i liked to make her mad. I remember acting up as a child and i clearly remember it was because I felt like I wasnt getting enough positive attention.
The reward system is great, but threatening to "take her to hospital" isn't such a great idea. I'm no psychologist but it's not a great thing to encourage a fear of hospitals/dentists/doctors etc...
Smacking only encourages violence and make sure you don't yell at her or call her a "naughty girl". Encourage positive behaviour.
I have always found self-education to be the best solution, so perhaps go and have a look at your local book store for some decent literature on child behaviour.

Very best of luck. I know how frustrating it can be, but take some time to try to understand her and why she is behaving the way she is.