Can I transfer from one top university to another? What are my chances? Is it worth it?

Hi. I’m currently an undergrad at a very selective and prestigious (~25% acceptance rate) liberal arts college. I got a 2000 on the SAT, and did kinda well (top 25% of my class) in a very competitive public high school, but a huge reason I got into my current college is because I’m a double legacy. The main reason I applied ED is because I’m a double legacy. But I’ve decided that I don’t like it here, and I want to leave. So my question is… will being at a very prestigious university help me get into other perstigious schools like Tufts, Rice, Pomona, etc. even though I’m getting mostly B+/A- at my current school and given my high school performance? Based solely off of my high school performance, it’s unlikely I would have gotten into any of these. Some of my extracurriculars:
Club tennis (HS/College), volunteering (HS/College), Ultimate frisbee (College), treasurer of Make a Wish at my current College, I had a job for 2.5 years at home.
Some other facts: member of LGBT, 770 on Math section of SAT, hoping to be a Math/Stats major.

My dad said I could only transfer if I go somewhere as good or better than my current school. I won’t go too into why I want to leave (greek life is a major aspect), but my question is: is leaving realistic? Is it worth trying? Thank you!

You have noting to lose by applying for transfer, and possibly much to gain if you are admitted.

But do spend some time working on ways to like your current place better. If you aren’t admitted anywhere on your parents’ OK list, then you will need to stay where you are. You need a plan for finishing up there if you have to.