I'm in a really similar situation - and I think for the same school! I had already committed to an interview at one school (they already booked my flights) for the exact same weekend the second school asked me to visit. I had to respond and ask for one of the other weekends, and they explained the same thing to me about faculty availability. It's unfortunate, but I didn't have a choice. Better than declining!
I do have two other interviews back to back that are literally across the country. Just make sure if you decide to book back to back, that you try to get as much wiggle room as possible in case there is bad weather/delays/cancellations. I'm a little worried about that myself!