I think the term gap year and your story are somewhat colliding and making it harder for you to make a decision. A gap year is usually a time to build maturity, or experience, or take a breath between high school and college. Sometime the student is admitted right out of highschool and then defers that admission for a specific amount of time (1 year). Situations differ, but in all cases a “gap” year (or years) is to pursue something that is closed-ended in time between two defined pursuits (university and college). What I think that I hear behind your story is a desire to pursue animation as more than just a pursuit, but possibly as a career. You are mature enough to acknowledge that you may not love it as much as you thought once you are really into it, but you just might, and are confident enough that you would be good enough to consider it a career, not just a hobby. But then you go onto to talk about it only in terms of a 1-2 year “gap” program that you wouldn’t finish.
I think that you are letting what you consider to be the expectations and norms of your family to discount a career that could be meaningfully to you and capability of providing a paycheck that meets all your needs. If this is the case, don’t be afraid to pursue art school, but do it with the intention of finishing. Don’t short-change the effort or your dreams. You may find out that after 1 or 2 years that it is not for you and you want the more traditional university path. You can then apply to schools, and you will be outside the “normal” high-school to college path, but will still have your test scores, grades, and unique life experiences that will make you a good candidate. But that would be your safety net, not the intended consequence of pursuing your giftedness.
Talk to your parents about it honestly, and understand that if their desire to pay for an ivy league education doesn’t carry over to art school, that is their right and don’t fault them for it. You can then go the traditional path first, and then maybe come back to animation, or figure out how to make it on your own. But if you are mature in discussing it with them, let them see your skills and that computer animation is a legitimate career, they just might surprise you.