Hi icemaiden, I do sympathsie with your plight, and the underlying situation outlined in your last post.
i am step-dad to two daughters, we certainly had our times when the oldest was coming up to and through her teens.
Any child will play one parent off against the other - biological, or inherited - and that has to be dealt with by a united front. You must boith agree a set of rules of behaviour, and back each other to the hilt, even if you feel the other partner is wrong - you can discuss that away from the child at another time.
Screaming matches are simply not on - either your partner lacks the parenting skills, or he feels inadequate, and argues with your daughter as a peer, which she is plainly not.
You need a four-way chat - where raised voices are banned - and a few rules are laid down.
First and formost - respect is given to all by all. That means no shouting by anyone at anyone. Issues will be resolved by conversation and explanation, with a chance for discussion first - BUT - the parent has the final say. This must be backed up by reasonable discipline and firm boundaries.
Ironically, children appreciate the very boundaries that they push against - it makes them feel secure - hard to believe though that may be.
Your partner needs to understand that adolescence is a hard time for your daughter, she is learning who she is, and occasionally wants to be seen and treated as the adult she will soon become, and at other times, be the child she still it.
He needs lots of patience, and to learn to read potentail hot-spots and deflect them - this will come with some guidance and support from you.
Anyone who feels unsure and out of their depth will react with hostility, and that means your daughter and your partner, hence their propensity to yell at each other. You need to encourage noth of them to get along, and be nice - which makes for a far more pleasant househild.
Do not on any account allow anyone to play they 'You are not my dad / daughter' card - jump on that from day one.
You must reasure your partner about his role in the family - and with you - but he has to know that he is the adult, and the fgood behaviour example is his to give, and your daughter's to follow.
Be patient - keep communications lines open for everyone, and you wil get through this - promise!