As a proponent of Home-education and a former classroom educator and advisor, I'll chime in on advising that switching now is probably not the time (sorry).
Instead, I would focus on getting your GPA up and figuring out how to explain the earlier low GPA in an "exceptions" essay. Even if you started homeschooling now and got a 4.0 (With clear proof a 4.0 was appropriate), it would simply be averaged with earlier work anyway. You need four years worth of work in your transcript - even if part of it is homeschooling work, you still need the work.
As already pointed out, it really depends on the specific college and as I understand it, College admissions offices are overcoming former prejudices against home-schooled kids and even seeking them out in some cases. However, at this late point in the game, leaving the school setting you are in and have been in for 11 years, looks more like escapism than an improvement in your situation on paper.
Focus on over-coming the challenges you have faced in the past so that you can speak about how you over-came them and are a better student now in interviews and in a short-essay response to, "Is there anything else we should know about you when considering your application." Umm and get those applications started!!
Consider these alternative "compromises" with your current school:
Go meet with your school district's guidance counselor/counselors. Get the info you need for your goals and location regarding the admissions process as well as brainstorm ways to meet your needs within your district or school's systems.
- Will your school work with you to grant an "independent study" so you can work your way through The Handbook of Mathematical Logic under the supervision of a cool teacher there at the school. Then you can skip out on Trig or beginning Calc (typical Senior year fodder for the college-bound) and not waste your time with it. You may be able to find a teacher who is willing to exchange being your mentor for a little help grading changing bulletin boards, making copies or other work around her/his classroom?
- If you are in Washington State look into the Running Start Program - which allows highschool juniors and seniors to take college level courses (at community colleges) on the state's dime and get both high-school and college credit at the same time (GPA applies last I knew). Even once you are in college there will be gen-ed requirements you may consider to be a waste of your time. This helps get some of that out of the way too. I'm sure at least SOME other states must have similar programs.
- Get in touch with AEGUS (you'll have to join) and see if they have any further ideas for you and if they have representatives that can help to advocate for you to get a superior education right where you already are.