When you say "father the bible described", you do mean parenting with love and grace, correct?
Children do not need friends, they need parents.
You entered her life as she is entering puberty. A hard row to hoe from the start.
I gained 4 step daughters when I married my wonderful bride. No boys ! So I'll share a couple of points that will help you from wanting to go out for milk, and never come back
Never take anything personally. They are humans with personallities. Sometimes they make it hard to love them, They can be mean, ugly, bullies, and evil. But they are your brides child, and God's children.
You are not alone. Your wife and you must parent as a unit. In the begining, my wife expected me to jump in and rule the roost, but I had to explain to her that I cannot come out of the gate like that until they get to know me, and more importantly, know that I do care for them, and they can trust me. From the beginning, my wife set me up to be the final authority. She exgagerated this ealry on by defering even the simplist request from the girls when the wanted something. She would say, you'll need to ask "me". In the beginning, the oldest, then "13" absolutely hated me and "mom" for marrying again. For the first year she would not speak to me, and when she asked for something, and mom set her to me, she dropped the request before she would ask me. While this sounds tyranical, and cruel, it was not. For example, when se was 14, she wanted a TV in her room. She refused to ask me. Her mom later told me that's what she wanted to ask, but would not. While we hated the thought of her having one in her room, about a month later I bought her a TV, and put it in her room. That was the first time she spoke directly to me with a "thank you". It took about 2 years before we could hold half a conversation, and she would accept help from me with her homework. This summer she'll 18 and out of high school with honors. She'll hug me on special days (without feeling for a softspot to plunge a knife).
If I can sum it up, the key was to demonstrate a parental unit that a single child could not drive a wedge between. The other three girls were younger, but they all have their little ways of trying to wedge between us. Guilt is the largest tool. The oldest used that on my wife a lot by "saying you ruined all our lives by what you have done."
While my wfe made me out to be final authority, she was very active in the decisions. Most disciple was discussed between my wife and I, and then given at a kitchen table meeting. Most of the the time the girl would storm off screaming. Let her ! Screaming is what they do
You must pick your battles, and them turning and storming off is NOT one of them. As the head of house, we must show more grace, and be humble in our servitude to our family. That is how you gain their trust, and love. On the other side, they must understand that disobiediance brings consequences. There is always something we could take away, and we have one time or another. ON season, when everthing was out of control. The girls were pretty much refusing to do chores, homework before tv, etc.. I came home one night, and my wife explained that she was tired of it. I walked out of the house with a pair of wire cutters and snipped the cable tv wire. One month without cable. 1 day was all it took for everyone to get with the program, but 1 month was the payment. They also knew there would be other extras from "stepdad" as he was also paying for their deeds because he couldn't watch tv either. Now they knew I was crazy. Prior to that they only suspected it.
And the most important thing to remember, do not get between the girl and her mother when they fight, unless the youth is completely out of control and disrespectful. You do have a duty to protect your wife. I don't know if you know, but females in a single house will sync up their cycles. Do you have a hobbie ??
No matter how ugly she is, you
The repect from the step daughters cannot be demanded, and can only come from them feeling secure, and loved.
Hope some of this might help ~ I feel your pain.
