Best way to 'handle' what would appear to be a belligerent 11 year old girl?

The behavior has to broken and reformed rather than enabled. It's a straightforward solution, but it does take a certain sort of deftness and mindset. Don't allow it to perpetuate, deny control(don't respond emotionally to the outbursts, stay calm and controlled) and punish the behavior(restriction can be an effective method for this) then enforce the better behaviors. (Usually done through a reward system of some kind, possibly reinstatement of the restricted items and then some small gifts of some kind after that)