Why won't she let me go out as much as my friends?

About a year and a half ago, I started going out alot with my friends, and about 7 months ago, got in trouble with the police a little but didnt get a record. I didnt go out with my friends at all over the whole summer holidays, and my mum and dad promised i could go out when i started school again. They made me move schools and wont let me go to a particular town ever again because of some small stupid things i did. Now its half term and I made some plans and told my mum beforehand my plans, and she's got a cough now, and is too ill to drive tommorow, and I didnt go out on sunday or today, so I said I would take the bus. She said no, because i'm not old enough. And I used to take the bus all the time. She would let me take the bus, but her word is always overidden by my dads, and he wouldnt want me to. he says he wants me out the house all the time but he hates me going out and wants me in the house all time, if It was up to him Id go out once a week. Everything she says now is based on what my dad tells her to do, or tells her what to say. She complains she always wastes petrol, but If she let me on the bus it would be cheaper. My best friend is 12 and she goes out every day of the week. I don't want to go out every day of the week, just more than I do now. I used to smoke, and now my mum thinks I smoke just because my friends smoke, and always makes false allegations towards my friends and thinks they are all nasty because they smoke, and that they have no personality. I did learn from my mistakes, but she doesnt trust me, and how can she expect to trust me if she wont give me the trust that I want?