What I really hate is that you are feeling all of this pressure and the weight of such irrational expectations. You have done extraordinarily well in HS, achieved on a very high level and that fact should be recognized regardless of if you get into any one college or not. DO NOT allow a college admissions officer who likely never met you be the arbiter of your worth/success.
Your parents need to recognize that the Ivy and equivalent schools have got exponentially harder to get into since they applied. Your HS guidance counselors should know how difficult it is to get in to these schools. AND even with the new standards, you are a solid candidate – that is a credit to your achievements to date. If you get into Yale that is great – if not tons of amazing schools will be thrilled to have you on campus.
FWIW I went to an Ivy school (which I never would have got into today) and my kids did not apply to any Ivy schools – and guess what – they both had tremendously happy, challenging, and successful undergrad experiences, both got into top grad schools in their field and both are doing very well. As you go through this process, try to keep you on the prize – which is not Yale – but is finding an affordable college where you can have a great expereince and get where you want to go in life.