With regard to ranking, it is important to understand how arbitrary the rankings are. There is an excellent article in the New Yorker (http://www.newyorker.com/magazine/2011/02/14/the-order-of-things) that should help convince your parents that the difference in ranking between Amherst and Williams is not “real.”
I don’t know Williams, but your goal of “recruitment to an investment bank” is definitely a match at Amherst based on what I have read. Coincidentally (or not) during our visit to Amherst a couple of weeks ago, two of the students we met mentioned that they were going to do summer internships at investment banks.
“The diversity might be a little overwhelming” - I’m sure you know intellectually that diversity is a major plus. I suspect this comment reflects that emotionally it may feel like a bit of a risk. Coincidentally (again) the day we arrived at the cafeteria, my D noticed that she was in the vast minority - for whatever reason, people of color at the cafeteria seemed about 80% of the crowd. It gave her pause to consider, “Is this my group?” During the rest of her stay, including another trip to the cafeteria the next day, she was able to meet (as you have) many people that she connected with. Having been accepted to Amherst as well, she is looking forward to the opportunity for personal transformation that diversity will provide. I hope you can celebrate this as a gift as well. The following US News article may help put the benefits of diversity into perspective http://www.usnews.com/education/blogs/professors-guide/2009/08/12/why-does-diversity-matter-at-college-anyway
Good luck with making your choice and congrats for being accepted to two great schools.