I think this little girl needs empathy above all else... time outs and punishments only enforce isolation and will re-enforce her feelings of being bad. In her previous home, the people who she loved most, abused and neglected her - she CANNOT trust anyone. So I can sort of see why she might flip... any closeness or love she received in the past, had the flip side of abuse. Sounds like classic disorganised attachment... seeking affection one minute and acting out the next.

I wonder what life was like for her after 2pm? When did her dad come come, what was her mum doing? Are there any triggers... the lead up to bedtime perhaps? Also agree with the posts above, small kids need to eat frequently and I would imagine she is probably exhausted from all the stress and trauma + new living situation.