Taking gap years for art school before attending an ivy league

Yeah, I don’t think this is an all or nothing thing. You don’t have to go to an art school to study computer animation; there are many comprehensive universities (including some competitive, prestigious ones) that offer animation studies within their art departments. There are USC and Carnegie Mellon, as already mentioned; there’s CalArts, if you are really good; there’s

Stanford (art practice & CS combined major)
Georgia Tech (computational media)
Emerson College
Northeastern University (within their art + design major)
Virginia Tech
Rochester Institute of Technology
Rensselaer Polytechnic Institute (RPI; there are three majors that may appeal to you)
Southern Methodist University (creative computing)
MIT (they have a minor in art, culture and technology…and of course there’s the media lab)
NYU
WPI

Once you have a bachelor’s degree, you’re actually ineligible to get another degree from most elite/top schools. The only one I can think of that would allow you to do this is the School of General Studies at Columbia.

That’s why the answer to this question

is definitely the art schools.

This is probably more doable - many art schools, especially for-profit ones, will accept you for a second degree. Better yet, you could probably get a master’s in animation after finishing your BA in something at a university. The question is whether you’d still want to pursue this in four years, but that’s fine - you’ve got time to decide.

Yes. I would argue that since it is your life, your dream is far more important than your parents’ dreams. However, I would also propose the suggestion that your dream isn’t so much to go to art school as it is to study animation on some serious level, which is different.