OP, it sounds like you have a solid plan. However, I think you would have a much easier time selling your parents on Yale than Princeton, given that the number of prominent conservative figures to come out of Yale exceeds the number from Princeton (and I’m sure, in your parents’ eyes, Princeton would be soiled by the likes of Michelle Obama, Kagan, Sotomayor, and a very active BDS group). Harvard’s also been traditionally very liberal, more so than Yale. It sounds like if you want to attend an elite university with your parents’ blessing, Yale is your best bet. Dartmouth is usually considered the most conservative Ivy, though, is also very generous in aid, and has one of the largest and best physics and astronomy departments in the country.