He's emotionally blackmailing you into being the substitute mother for his kid, who he has parented to behave like an overgrown toddler. Sleeping until two? Breakfast in bed? Everyone hanging around until she deigns to bestow them with her presence. No wonder you are pissed off OP.
It's not your job to be her mother OP, just to welcome her when she is there. My parents have more than five marriages (less than ten though!) between them. By her age I understood perfectly well that blended families take compromise from everyone. She's not a baby, she's not far off adulthood, she also needs to take some responsibility for fitting in. Really though, the issue is with your husband. How dare he effectively tell you off for not wanting to pick up his slack.
As usual the step mum threads are rife with misogyny. You can practically play sexist bingo. Remember the rules OP.
You must give up your life as soon as you partner a man with children (he will retain all of his freedom to behave like a single man).
You must do absolutely everything to parent a child who is not biologically yours. Whilst not interfering in any way as you are not her real mum.
You must put your needs aside so that your husband can be free to party with his mates. For God's sake though, make sure you put the children above everything. You are a Mum now. Don't you understand that, you're not really a person in your own right.
It's imperative as a woman with kids that if you do split, you facilitate a relationship with the father and model good behaviour. Yes he may not want them for any real chunk of time but as a man, it's his right to be a Disney dad. In this instance he's gone on to remarry and have two more children but as a woman you would of course be expected to remain single. As someone on this thread quite rightly pointed out, the biological mother in this case may well be at fault and causing the teen's bad behaviour as she may have had the temerity to get a boyfriend (she might not have one but let's blame her too just in case, she is a woman after all). Obviously she doesn't realise that her role as a person has to be subsumed until all of her children are grown and gone and she is left alone like a forgotten incubator.
If you are a woman, you simply can't win. The double standards are rife.
It's no wonder patriarchy reigns strong is it, when there are just SO MANY women willing to do the job of oppressing and undermining other women for the benefit of men.
I really hope you give your DH a piece of your mind OP. If my husband treated me like some sort of babysitting skivvy, I'd be seriously reevaluating the relationship and explaining to him just how very little I like him at that point.