Using that LOR for that ONE place is redundant. They should already know you from your away. You're pretty much wasting the letterwritier's time.

Think about it. You send LOR's out from faculty at your home program. does that mean you only have interest in your home program?

Agree with Agent13. On your interviews, most places are going to ask you where you did your away rotations, so they're going to find out anyway. You just have to tell them what you liked/didn't like about your rotations, and how you think their program compares and contrasts with it. Programs know you are only able to do 1-3 aways, depending on your school's policy, and as long as you are sincere in making them think you are interested in their program, they may still rank you highly. (I put a program where I did not rotate at the top of my list and matched there.)

thanks for the replies. i didn't think that logic made sense

It's good to have a variety of letters from different places. It will be more effective to have multiple independent people recommending you, opposed to attendings at the same program who work together.

The letter writer will sometimes also write something like "we'd love to have this student as part of our program" or "student will be ranked very highly at our program" and this will make you more attractive to other programs.

Also, a lot of these attendings know each other from residency/conferences/previous jobs, and having a letter from someone the interviewer knows is a huge advantage. Which is more likely to happen if you have letters from different places. Interviewers would sometimes see a letter from someone at a place, and ask if I worked with his friend, Dr. so and so who is also there.

Also, when I was going through the process several years ago, I had several attendings make comments about how positive it is to have a good letter from an away rotation. It is much easier to look good at your home institution than one in a strange city, hospital, etc.