As a father of step-daughters, I know how difficult they can be.
i think you should try to make more of an effort to build a relationship with your daughter (I have no time for the 'step' tage - they have a 'father', but I was always their Dad, an important distinction).
If you have a daughter with her mum, that can - and probably has, made her feel pushed out, as evidenced by her lack of personal pride. She may be unable to articulate her feelings of being less worthy of love and affection, and so manifests them, with the unpleasant behaviour you have outlined.
Why not try and taker her out - just the two of you, maybe to the pics or for a pizza - so she has some individual attention. Small children can be demanding of attention, which can be misinterpereted by sensitive teenagers, so try and redress the attention balance, and ensure your wife does as well.
Some regular affirmation of love and affection will start to build her confidence.
Get laundry and waste baskets for bedroom and bathroom - basic with teenagers in the house.
Buy her something new to wear, and when she puts it on, make a big fuss about how nice she looks - it may feel OTT to you, but it's what teenagers need - something to counteract those horrible feelings of insecurity and paranoia.
It takes time and patience - but it will work - trust me, I know!