Katie
My heart goes out to you - this part of TBL is no fun. I have had only one similar experience and, as with most things, everything ended up being okay in the end.
First and foremost, the students who came to you are probably hoping that you will move the other student to a different team, or that you will 100% side with them, creating an uncomfortable power dynamic between the teammates and between you and the students. They may also be hoping that you will lower the other student's grade. None of these things need to happen.
I think one of the worst things you could do would be to rearrange teams. So I hope you don't choose to do that. In my case, I had a chat with each of the offending parties, and basically said that they would remain in the same team for the whole semester, so it would behoove them for the sake of their sanity and for their grades to reach a truce or a compromise with each other. I explained that in the workplace, a similar situation may arise, and learning the skills to deal with it effectively will be extremely important, both personally and professionally. I reminded them that their peer evaluations were worth a large portion of their grade (in my classes it ranges from 17-20%) so it would be smart, if they wanted to pass the class, to make adjustments to their own temperaments and ways of doing things (i.e. completing the application exercises) but also to be honest on the peer evaluations. I have never "touched" a peer evaluation - that is, I have never changed someone's peer evaluation score.
I would reassure the worried students that you will be monitoring (I assume you walk around the class during application exercises) the situation but that they are also responsible for making the team work well together - the team's success does not depend on everyone being happy and getting along together all of the time; it depends on teammates to show maturity and respect when disagreements arise. After chatting with both parties, I also reminded them to arrive at the next class with a clean slate. Gossipping and moaning and complaining about it to others (also known as co-ruminating) would only make the situation worse.
In my case, after I had the conversation and one of the students got dinged pretty badly on her peer evaluation, she changed her behavior and her teammates were also less hostile. It was amazing, actually - they handled it better than I expected.
Anyway, hope this helps some. Good luck!
Meghan Gillette
Doctoral Candidate
Human Development and Family Studies
Iowa State University