Okay, if you HAVE to talk to them both together...
Have a calm, rational discussion with the both of them, where you mention specific incidents that upset/anger/offend you, explain that this is making it difficult for your subordinate as well, and that some things need to change.
Don't make ultimatums unless you really want to leave.
It sounds to me like she's petty and childish enough that having the conversation could make things worse, to the point where she tried to force you to quit.
Bottom line: don't discuss it with her unless you're absolutely prepared for the WCS of having to find a new job.