Not everyone has the ability or desire to post on an internet forum asking strangers for help. Some for fear of embarrassment or ridicule, others because they want to keep their private affairs ... well, private. I'm not seeing ANY fault in stepmom from trying to find out some answers. To castigate her seems cruel and unnecessary. Personally, I wish more step parents WOULD be actively involved and concerned with their step kids' lives. I know of a great many kids who would have enjoyed that, too. As a foster parent over the past 16 years I have heard and seen a great many stories and in many of these homes, a STEP parent was the only REAL parent many of these kids had. Yeah, they cannot generally act in any legal capacity in court, but, their involvement in the child's life can make the difference in that child's life.
As for dad, I too have gotten the impression (maybe incorrectly - I'm reading this on a small screen laptop) that some people here seem to think that if dad were to quit his job to be home that would somehow be beneficial. I have seen the results of that sort of thing and it might mean dad is home, but it might also mean that they end up living in the back of a van. Dad shouldn't need to quit his job to deal with a situation that his materialized recently.
I do agree that it sounds as if this child appears to be a tad on the self-important and spoiled path and will be a problem whether she's at mom's or dad's. I caught in at least one of these posts that she had run away to her boyfriend's house, so it seems pretty clear that she prefers to play house and no longer play child. Unfortunately, given daughter's behavior, rehab, and the lack of any real support from the police (and I was not aware that LA was one of the states where the cops cannot drag a 17 year old home ... make that THREE states that are messed up, now), there may be nothing much to actually be done except wait for her to turn 18. Of course, maintain the missing/runaway report and TRY to bring her back home, but, I suspect that tracking her down and trying to drag her to mom's or dad's only to have her runaway again will be akin to banging your head against the wall.
Sadly, she will likely be with child soon, and very well on government assistance. Hopefully boyfriend is a guy with a great job and his own house at age 18 or 19 ... but, I somehow doubt it. I'm seeing a trailer next to the bayou with folding chairs for furniture ... but, maybe that's an exaggeration.