Sorry, I've skimmed through the posts.
If you are her manager, I'd make it perfectly bloody clear to her that YOU decide when she can leave site.
It is simply not acceptable to 'go home for a few hours' because someone said something you didn't like.
Sounds like she needs a good shake!
As their manager, you shouldn't be in their coffee-making-club anyway. You have to maintain some distance.
I'd schedule a one to one with this girl (and the rest of them) and get some basic ground rules in place.
For sure, you shouldn't have shouted. You already know that.... but this girl's behaviour is not acceptable either.