You can show your parents this:
https://www.binghamton.edu/admissions/academics/outcomes.html
Then explain to them that Binghamton has a 69% on-time graduation rate versus 30% for Cobleskill:
https://www.collegefactual.com/colleges/suny-college-of-agriculture-and-technology-at-cobleskill/outcomes/
https://www.collegefactual.com/colleges/suny-at-binghamton/outcomes/
Show your parents how difficult it is to get into Ivies these days. Here are stats on Brown (which has a higher acceptance rate than some of the other Ivies): https://www.brown.edu/admission/undergraduate/facts
Sometimes seeing facts in black and white can help us parents to understand what admissions truly looks like these days. It definitely helped me. Maybe show all of these stats pages to your sister, too.
Now, what do YOU want to do? This is your life. I understand that your parents’ opinion is very important to you. But you have to live with your choices, so make sure you have taken a moment to think about what you want. Forget the whole prestige thing because the day after high school graduation you won’t have to worry about what your peers are thinking. What do you want to do in the long run? What kind of career do you want?
There are many paths to get there, and Binghamton can probably get you wherever you want to go. Do you want to go to Binghamton?
And yes, if you really want to be a doctor, major in something other than biology as @MYOS1634 suggested. Maybe Math? Music? Psychology? Anything! Just go to the pre-med meetings and make sure you take all the pre-med requisites. You also want to volunteer/intern in a medical field. Med schools expect that these days.
You are an intelligent, worthy individual. You can do this.