Four moves for mediating without making it worse, not a general essay on conflict resolution.
01
Talk to each of them separately first
Getting both sides before you're in a room together keeps you from being ambushed by a dynamic you don't understand yet.
02
Don't referee, name the pattern
Your job isn't to decide who's right about the specific incident. It's to name the recurring pattern causing friction and get agreement on how to handle it going forward.
03
Bring them together only once you have a shape for the conversation
A joint conversation with no structure usually turns into two people re-litigating the same disagreement in front of you.
04
Follow up in two weeks, not never
Conflict resolution that isn't checked on tends to quietly reopen. Put a real date on the calendar to see if it held.