Interview conflicts - Help!

[kalella]

I very recently got an interview at a top school, and it is one day before an interview I have had scheduled for a long time at a school in a different part of the country. Initially I tried to reschedule the more recent one, and the person I contacted was very receptive but had to wait to see if one of the directors would be available on an alternate date... they are still waiting and apparently will not know if there will be an alternate date until after when I am supposed to arrange travel, etc. Because of this I emailed the other program and asked whether I could reschedule that interview, which I figured would be much easier to reschedule in general as it is within driving distance and I do not have flights booked or anything like that. However I got a response that since flights were booked and meetings were set up, it would be much better for me to attend the weekend than to visit on a different day. I don't know how to handle this now, because I do not think I could possibly make it to both interview days, and I am not ready to choose between these schools as they are both top choices of mine. I don't want to lose out on an opportunity due to scheduling. Any advice on what I should do? I really want to get this solved ASAP.