Sorry Facefacts not got much advice, but it sounds a bit horrendous. The situation sounds awful.
Can you get her to attend some sort of family therapy with you? Do you pay her an allowance or something? Can you make attending a session or two or more a requirement of getting the allowance?
Maybe having a third party know how badly she behaves and having a chance to express how she feels, why she feels the need to behave in a certain way, could be useful for her.
My dd is only 11 and is quite a handful at times. I really wonder how it will all pan out when she is older, I really try with discipline etc but sometimes kids can just be quite hard.
When she is not flouncing in or out or demanding her own way etc, can you sit down and try and get through to her about how destructive this behaviour is?
What is the plan for when she turns 18, university, work, further study? will you and her dad be supporting her? Would her getting a part time job where she has to follow other people's instructions be useful to her?
I would also post something similar in teenage year if there is a section.
Is she like this now and not when younger? Have things changed in the family in some way to exacerbate this?
Can you and your daughter draw up some kind of an official agreement that would give her some of the liberties she would like but would be work-able for you too?
Young people can find it very hard to see things the way adults do, and there may be reasons for this.
www.theguardian.com/science/2014/sep/05/teenage-brain-behaviour-prefrontal-cortex
In your shoes I woudl have a very good search on line for all things that would speak to you about how to work this out with your dd. Enforcing things onto her is not working and is adding extra strain into your relationships. Can you find the compromise you need together? Even if she will not go to family therapy, counselling or relate or whatever with you, could you go and get advice on how to handle this?
I am sorry if this is all very basic and beyond where you are but take a look at some of this stuff....
www.positivediscipline.com/articles/teenmotivation.html
understandingteenagers.com.au/blog/the-7-secrets-of-motivating-teenagers/
Can I ask if you have any other children?
Can I ask if there has been any big family tragedy at some recent point?
If your dd has always been this way then it may be that things will not change any time soon, but maybe she has her ups and downs and you need to catch her on an 'up' to deal with the issues that happen on the 'downs'.
I also wonder (this is just an idea that has pinged into my head) if she sees you and her dad as some sort of 'unit' and is trying to divide and conquer! I am not sure if that is relevant but if it is then I would get some professional advice on how to deal with it. (My gut feeling would tell me that rather then be a unit that crumbles and lets her feel she can break things apart whenever she wants to, and rather than being an impenetrable block that she sees as an ongoing challenge, it MIGHT be better for you both to work out ways for one or other of you to deal with certain small issues and try and see if it is possible for her to work with you one on one rather than it being her against you two.
Good luck, Facefacts.