@ayyyyy I will concur with others that leaving school early for homeschooling your senior year could hurt your chances for Yale but in reality your chances aren’t very good in the first place. Yale is a lottery school. Nobody had a good chance of getting into Yale. Staying or leaving could be a wash either way. If you stay you look like everybody else. If you leave it could raise eyebrows or it can help you stand out. Depends on what you make of your final year and your essay.
As one poster mentioned above, you sound desperate to leave, but you are stating it is for academic and maturity reasons. That is not coming across in your original post. You sound like a whiny child who thinks she is better than her peers. That may be true but I would not show that attitude with the adcoms.
I would guess there is more going on. Most kids don’t have the need to leave their last year at school to fulfill their destiny. But if there is something going on that makes you really feel that there is no other choice (something other than thinking you are better than your peers and wasting your time doing high school academics) then I would take the time to make sure your are doing the very best homeschool curriculum you can. For this I would get off this message board and visit homeschooling boards whet you can get good advice from more families than you can here.
I would beware of dropping from the rigor of an AP program to coursera. Sure you can get certificates but you are an anonymous person who can choose to work hard or slack of and will have no grade to show the adcom which one you did. You may want to find a way to continue with AP courses outside of school so you can prove that you can handle the rigor without running away, because right now you look like you are running away. This is why I suggested virtual courses. You can do then on your own time which will allow you to be away from school but still show rigor your senior year. If you chose to build your own courses your are going to have to find a way to show rigor and that is going to be tough. Many HSers use SAT subject tests to show mastery of info but they do it before senior year.
If you decide to look at virtual as an option the CA UCs have a place where you can look and see courses that they have vetted and approved. It could help you choose. If you don’t want to go virtual I would find a place where other homeschool families can give you advice on how to make a very very good course. I don’t know much about NY but her in CA we also have co-ops that allow homeschoolers to take a course once a week in small groups. You might look for that so you can get guidance and recommendations. They are not very expensive and allow you to do lab work and have discussions outside of home study.
One more idea is to do a true distance learning like Oak Meadow where your can purchase individual classes and correspond with an instructor. They do their AP through CTY which is Johns Hopkins and for non AP independent study you can also buy their curriculum. There are many ways to go but yoy need to get more ideas than simply Coursera. Go to the homeschooling forums where people discuss curriculum and ideas.