OP, our situations sound eerily similar. I'm 20 with a disabled brother and quite controlling parents (or specifically mother), though I live somewhere much less expensive and don't have to commute.
Had to defer uni and move back home this summer. My mum would also go through my room, not allow me to go out (I did anyway), and generally treated me like an inconvenience. We never had the conversation about rent - I wasn't there long enough - but would have contributed to the household according to my earnings.
I did exactly what PPs have suggested, went on spareroom.com and found a houseshare about 20 mins away from my parents' house for 420 pcm including bills. Luckily I was able to find a landlord who doesn't charge a deposit, just a fee (which was bloody lucky as I was broke). It might seem like madness renting that close to my parents', where I would pay a lot less and could save more, but it's been the best thing I've ever done.
Yes, its been bloody hard, but I've learned a hell of a lot about budgeting, organisation, and, dare I say it, 'the real world'. I've also had a fantastic time being young, living in a city, and having some proper disposable income for the first time ever.
As PPs have said, your £300 rent and £600 commute plus savings leaves you in a good financial decision to move. It's annoying that the move with your cousins fell through, but get back on the horse. Start by registering on Spare Room - takes 2 minutes. Baby steps.
One thing I have to pull you up on is your comments about your brother - I don't see how he fits into the situation with your parents. I know I will have to make provisions for my brother's care one day, but I don't resent that fact in the slightest and he is never involved in disagreements I have with my DPs (and there are plenty). He just doesn't come into the equation.
Feel free to PM me if you want any more specific advice.