There's so much going on in your family! You acted appropriately not letting her sleep over at the friend's house, the mom doesn't have great judgement. Take your daughter to lunch, just the two of you, and lay it all on the table. Your reasoning, your adult take on the way the situation should have been handled, your concern for her well being. She's at that transition age, young enough for major guidance but old enough to make some decisions and choices(after discussing the options with you). She may be overwhelmed and frustrated and feeling left out due to all that is going on with everyone else in the house. I know it's hard. Don't give up, and stick to it. My mantra for life is 'this too, shall pass.' My oldest son was really rough, and it at last took spending a night in detention to finally kick him right; you would never know today 6 years later the awful time I had--I told someone it was like riding a tornado. He recently told my mother that he was so grateful that I never gave up pushing him in the right direction while allowing him the freedom to make his mistakes. That made me cry. His 4 siblings were a piece of cake. Best of luck.
