To a lesser degree, I am living the LW's life. My husband did not have custody of his children but we had them in our house frequently, and my husband maintained financial responsibility for his daughters. I think Prudie missed the point somewhat in her response. Step-parents are NOT parents, and PARENTS must have the ultimate responsibility for their children's discipline and behavior, NOT the Steps. It seems that Dad is allowing less than stellar behavior out of divorce guilt (something I've seen often) and therefore, Step-girlfriend feels she must step in. Frustrating as it may be, they are not HER children and no matter how RIGHT she may be, they are not going to respect her ... at least not until Dad show how that works.
LW has two choices. Cool off and stay out of it, and the daughters will probably go away eventually (which I doubt is possible given the tone of her letter ... her staying out of it, I mean). Dad is going to reap the seeds being sown now. My husband has a very cold relationship with his daughters as they only contact him when they need money. His "hands off" approach (his feeling was "they'll contact me if they need me") has resulted in them drifting farther and farther away from him. I was available and friendly but they were never interested in a relationship with me, and this was further complicated by the fact that their mother worked hard to make sure that the only information they received about their father and me was negative.
Choice two is get out now because she cannot tolerate a living environment over which she has little control. You can't teach respect .... you can only demonstrate it and earn it. Difficult with teenagers under the best of circumstances ... impossible with a "hands off" father in the picture.