You raised two other daughters without getting that result, so you must have some knowledge about good parenting. One thing to consider is what is different between the environment my older two daughters were raised and that in which my youngest was raised? Is there a different father? Is there some different stressor (is there a possibility that she's being bullied at school/does she have a learning disorder which might be slowing her down as school becomes more demanding/is there instability or chaos - not of her own making - in her life, etc.) This is a clear starting point for your own analysis.
I don't know what I am doing wrong.
Parenting = guilt. If ever there is something wrong, a conscientious parent always assumes they are doing something wrong. And, I'm sure you are doing something wrong; every one of us has done at least a few things incorrectly. This doesn't mean you're the cause of her bad behavior.
I hope you will get a lot of advice on how to discipline an adolescent more effectively (if you don't, I'll edit my answer to add that.) Clearly, learning to disengage and set consistent boundaries with consistent, effective consequences is very important, as are learning new, positive rewarding interactions.
However, sometimes there is nothing that you specifically did "wrong". That is the case with a group of psychiatric disorders called disruptive behavior disorders (DBD), perhaps the most common of which is Oppositional Defiant Disorder (ODD).
Even usually well-behaved children can be problematic at times,
especially adolescents, but kids with ODD show a consistent pattern of angry and verbally aggressive behaviors, usually aimed at parents and other authority figures, such as teachers, babysitters, coaches, police officers, etc.
It can be difficult to know when someone just has problem behaviors versus ODD. Three behaviors consistent with ODD are deliberately
annoying and upsetting others, an inability to take responsibility for their wrong behavior* (always blaming circumstances/others for their mistakes), and being spiteful or vindictive.
The reason I jumped to ODD instead of the usual advice is that you mention
- she causes so much family disruption that only one of you at a time tries to deal with her
- she is having problems at school
- her arguments are excessive for kids her age (she dials 911 on you)
- she seems to act out spicifically on authority figures (adult siblings/parents/teachers/babysitters.)
If - if - she has ODD, it's important to find out, not to put her on medications as some are quick to point out, but because there is a systematic and helpful approach to ODD that has already been shown to be of benefit, which involves teaching coping skills to the child as well as new sets of interactions on the part of the parents.
Please have a look at the two references below. If you find she fits the pattern (some exploration of her behavior with teachers at school would need to be undertaken first, though), please enlist the help of a competent child therapist who can do a thorough evaluation of your daughter and the home environment.
ODD:A Guide for Families by the American Academy of Child and Adolescent Psychiatry
Oppositional Defiant and Conduct Disorder: A Review of the Past 10 Years, Part I