You sound as if you would prefer to go to York but are feeling guilty that you might be letting your parents down by not continuing where you are.
If you go to York, you could have a fresh start and you would be at an advantage because you are already familiar with a lot of the material in the first year of the course.
That said, you would essentially be paying to re-do the same - or a very similar - course in different surroundings. There is also no guarantee that, despite your intentions, you will end up with better results from York than you got from your original uni.
If you are genuinely unhappy where you are - and have good reason to think that you would continue to be unhappy next year - then you would be better to change universities and go to York.
A few other things to consider might be that you would be re-doing the first year with people who are new to university. Living away from home with new people will probably be a fresh and exciting experience for them, and you might not feel the same way any more, as you've already experienced freshers' week and meeting/living with new people. You would probably have more in common with people who've had a gap year than those who have come straight from school - and do you want to have all those "where are you from and what A-levels did you do?" conversations again!
Another thing to consider might be how you are going to explain the apparent extra year/change of uni but not course to prospective employers in 3 or 4 years time.
Are you sure that you would have exactly the same tutors next year, and that there is no chance of you getting experience in industry if you stay where you are?
If you want to go to York, think that it would really suit you and are certain that you want a completely fresh start, then I think that you should go for it; as you've said, it's your life, you're not enjoying it and there is no point in only having bad memories of your time at a university you hated.
Good luck with your decision!