Some things are more important.
The values your family are instilling onto you aren’t your values and I like your values.
I don’t know what a respected university is vs another - but say you go to Hofstra instead of Harvard.
You’ll get a degree you earned, can be proud of.
Let’s say you get into Harvard by hiding info ? You’ll be bothered every day - because you’ve developed fine values.
Btw you don’t know how any school will view you - but you need to live with your decision.
You want to be truthful.
Someone else wants you to cheat.
It’s sort of obvious (to me) what the answer should be.
Good luck and it sounds like you have a lot of growth and maturity and I’m sure it will be seen.