It's hard to say although I can't imagine being away from your family isn't in anyones best interest. Yes, I think itis pretty normal for teenagers and parents to argue cos teenagers turn into little monsters who grunt, scowl, don't listen, answer back, leave a mess, complain when asked to help out SO it's easy to see why parents get cross. Calling you hopeless isn't really nice of course but us parents say things we don't mean when we get to the end of our tether. I'm sorry darl. I"m sure you know if your Mum is a big meany or whethr she is a caring Mum who lost it. It sounds like you might think time away is a cool thing to do. I suggest you talk to her when you can tell she is relaxed and in a receptive mood. Tell her that you want to try harder and hope she does to so that you do not argue so much and tell her how it makes you feel when she says you're hopeless. I have had days when my kids wouldn't move in time for school, not taking pills, doing treatments, leaving rooms etc in a mess and I have cried all day cos all I've done is yell before school but I'm sure alot of other families are in the same situation. I Love my kids more than anything in the world but teenage years are hard. I wish you luck, you must make an effort too and know that you are certainly not hopeless an in a few years time you and your Mum will probably have a laugh and enjoy each others company.
Best of Luck