I totally agree with all the replies to your question. I'm a bit more long-serving host with 187 reviews, almost all positive and I've had only the best experiences with the two or three odd exceptions. These exceptions were exactly like the booking you described - lots of discussions, extra wishes, payment issues etc., very high demands while staying and feeling really uneasy on my side. Plus negative reviews for silly things like offering only a jug of tap water instead of a brand bottle or storing my laundry in the bathroom (in a closed bag which must have been opened to see what's inside!). I'm sure that your instinct about this being a high-maintainance and impossible-to-comfort guest is right and I'd recommend to not accept any discounts or prolongations - chances are that this will not aid you in having a nicer experience or a better review.
So what to do? From my experience, it's always best to be open about concerns. If I were you, I'd try to get rid of that booking. Of course you can't cancel without being penalized but I'd simply address in a positive way that you feel that you might not be able to meet her expectations and she might have a better experience by cancelling with you and find another host. If you put that really nicely I see some chance that she will follow. That won't work of course if you have a strict cancellation policy and it's too late for her to cancel (I always recommend to set cancelling policy to maximum relaxed) or if she's one of these persons that go for the best price and expect maximum service anyway. If she insists on staying with you I'd write a very welcoming invitation and take her out for a drink and talks on the first night - this might be a turning point or at least will raise the bar for her to leave you a bad review. And even if she does, you can comment on a not so great review and if you do that nicely and friendly future guests will see that you care about hosting and have your own style, which will definitely help in attracting more like people you love to host.
I learned from these very few not so great experiences and adjusted my listing accordingly, stating clearly what kind of guests I prefer (though everyone is welcome) and pointing out what I can offer and what not. Be open, friendly, and communicating, but stay true to yourself and don't try to to accomodate to everyone. I believe that this is the best strategy for attracting nice guests and have great times with them - at least this worked for me.
About discounts: just don't - if your guest demands that without further reason it's sheer blackmailing I believe and I don't want to have guests who think they're in a "buyer's position" and aim to have the best deal by competition. And while discounts are possible here, it's absolutely not a "common thing". Like you, I have the cheapest price around but for me that's because I want to have cool low-budget backpacker people and not stingy trolley-pushers looking for the cheapest alternative to a hotel - and my listing has a hint on that. I do give "friendship discounts" to people travelling on a shoestring and writing really nice requests but not to Uncle or Aunt Scrooge.
Hope I could help a bit and all the best to you from Munich, Germany,
Hagen