My 16 month old niece is 'terrorizing' everyone! Is this normal?

Set of by the slightest thing, she is biting, pushing, hitting, beating kids with toys, etc... Very physical child, dare I go so far as to say violent. My daughter is getting the brunt of it since they've lived together since Niece has been born. It's gone from Just my daughter, to my niece attacking me, her mother, her father, other kids at daycare, everyone. She's unfazed by anything. Time out infuriates her, and she goes immediately back to her behavior. (time out isn't something we've tried once and dubbed it a failure, we've been doing it for months) She gets set aside for one and a half minutes, asked to apologize which usually leads to a hug, then goes about her business, and gets aggressive again shortly afterward. Day care has threatened to kick her out once, and we don't want that. We are looking for opinions, suggestions, first hand experiences.... Help, please. Her mom is a first time mother, I have two kids, one 2 and one 6months. My 2 year old is a dream with mild tantrums. My father tended to my brothers by physical reprimandation. Which I'm not saying is good, or bad, it just worked for them. My sister doesn't feel comfortable with teaching 'no hitting' by hitting.