Do not feel like a failure - the teenage years will destroy you if you let it.
I agree with the posts regarding backing off with the homework and establishing some ground rules at home.
My DS, just completed GCSE's, did hardly any homework for all of his secondary school. I did goto every parents evening, much to his disgust, and talked with the teachers re progress, concerns. When GCSE's kicked in, they start in Year 9 at his school, we focussed on practise papers at home. In Year 11 I discussed with each teacher what he would get at school and which subjects to focus on at home. Was there any point me trying to get him to do study for all the subjects when only 2 needed the extra time.
DS decided very early on he wanted to be an electrician, yes he was capable of getting A's at every subject but he didn't need it. He wasn't going to university (had my own tears at that but got over it) not doing A Levels. He needed 5 GCSE's at grade C including English and Maths and got 14.
My rule for DS was 'as long as school didn't contact me I would leave the decsions to him but if school did contact me he was grounded for that week and I would get involved with his homework plans'. On the quiet I encouraged school to contact whenever there was an issue - eg deadlines not met. I was lucky with his school, it was a definate 'we' that got him through.
Regarding your DD - is she sabotaging her future or is she bright enough to know what she needs to do and is doing it in school. Have her progress levels dropped?
I also agree very much with Chloe74's post further up and also pick your battles. So what if she doesn't tidy her room, so what if she doesn't wear a coat, if she gets wet it will dry. Pick your battles - she is only in Year 9, you have got to get through to the end of Year 11, at this rate you'll be exhausted by Christmas.
The teenage years are awful, heartbreaking, make you question your own sanity but you are not the only one going through this. Start talking to friends with children the same age. It doesn't matter if you are a multi millionare or do not have two pennies teenagers are teenagers and nearly all parents will be expereincing to some degree what you are.
Sorry for the long post but DS has just tunred 17 and even 6 months ago I never thought that for one minute we would be where we are now. It does get better, it may get worse but it does get better, not overnight but eventually the time in between arguements, flare ups does get longer.