@AirbnbDallas : Here are some of your statements:
"This has been by far the most difficult guest I've ever had." [There it is in a nutshell.]
"When I suggested she find a more suitable accommodation she told me it's hard to find a place with another woman." [And how is that YOUR problem...]
"She became irate..." [Whaaat?! She is a stranger, a "guest" in your home and you cannot allow her to take the liberty of displaying such a reaction!]
"I want her to leave...and she seems unwilling..." [And whose home is it?!]
I just don't know what is holding you back from booting her out. The A/C is only the first of many more issues you will be facing with her. Surely the money isn't worth giving up your previous calm existence and peace of mind.