Honestly, I would take a little time, if you have not already, and set up a proper safety net.
What I'd -really- do, is move out first. At least get a job if you don't already have one.
I don't know what your situation is or which country you're in, but you could also try getting scholarships and grants to go to college. If you're in certain countries, college isn't really going to cost you.
I lucked out and got a ton of great scholarships in high school, and one of them paid my entire first 4 years of college. I also got thousands of dollars per semester from grants. You should research stuff like that, if you're interested in college at all.
College is also a good place to transition. I was too much of a wimp back then to start HRT (on it now though

), but colleges are some of the most accepting places. I know at least 4 transpeople from my days in college. None of them had issues, with staff or other students. I've also heard many stories of people coming out and transitioning during college, and having great success with their peers and instructors.
I'm only just 25, but trust me, you should really think hard and try to plan carefully for the future, and be ready for your plans to need to change.
Without knowing more about your parents it's hard to say what you should do. I know she said 'what you do when you move out is up to you' but I don't know just how against it she actually is. Does she seem ultra-against-it?
You never know if they'll come around.