I want to add a big hug here too. I detest conflict at work. Really really really detest it. One day maybe I'll tell you about the girl who worked for me that was such a nightmare in my first ever management job - she turned out to be involved in the UK's biggest serial bigamy case. No, I'm not kidding and yes I sprayed coffee everywhere and choked when I read that!
I can't do better than echo everyone here's sentiments. Stick with it, the mediation is often a good thing. I went to mediation with this employee as previously mentioned. She was outwardly and deliberately hostile, which showed my human resources and my direct line manager that it actually wasn't me that was the issue, it was her.
Hang in there, and when you feel like your head is gonna explode with it all, count slowly to five while breathing in slowly and fully then out slowly and fully. By the time you've counted the five you should have taken a deep and slow breath and let out a big slow breath too. I find this helps a lot, takes me 2 seconds to suck the air in and by the time I reach 5 the air has gone out and I've calmed enough to carry on.
Good luck and more hugs =D