First of all, based just on the information given, we don’t know that it’s a personal issue. We were only told they had a bad falling out and it could be due to a job related issue. (Salary differences, unfair workload distribution, favoritism, finding out someone said negative things about them, taking credit for another’s work, or any number of other work related issues.) In fact, KimodoDragon may not really know what the real problem is.
Even though I don’t know the specifics of why Harriett doesn’t want anything to do with Karen, the information about Karen being an instigator and her snarky gossip gives me a clue.
KimodoDragon, sorry but I don’t think it’s up to you to tell another employee how to behave. Where is the supervisor when all this is going on? Has anyone complained to the supervisor (or HR) about the childish antics and the tension it has created (apparently for a long time)?
Aside from needling Harriett, Karen also seems to be trying to cover herself (“Hey, I’m just trying to be civil”) and doing so in a junior-high school way. While I don’t condone Karen’s behavior, Harriett is not completely innocent. Being civil with other employees is a requirement in the workplace. While Harriett doesn’t have to be friends or even chat with Karen, the silent treatment is unacceptable. Karen’s “say good morning to me or I’ll keep harassing you” game is also unacceptable and needs to stop. Someone in management or HR needs to intercede and pull both Harriett into a conference room and explain that to both of them. Until someone officially complains it appears nothing will change.