You said, "I will book the hotel and you can pay what you think is fair." In the end, she paid you what she thought was fair. And you are surprised because?
Your fair and her fair are not the same. It is often true that people have different concepts of fairness.
I actually think that you are in the wrong as well. She was upfront with you about having a $500 budget for hotels. You booked hotels that exceeded her budget and put her in the position of not being able to pay her fair share. That was not very kind. Is there a reason why you could not have booked lower rate hotel? If you had matched her contribution equally, you still would have had $200 a night for a 5 night trip. Even in NYC, you can book a decent hotel for under $200. It might take some research, but it can be done.
Also, frankly, it is not for you to determine how she should prioritize spending her money, which you are doing when you say, she has 3 cars and buys her kids expensive outfits, so why can't she pay for this? You have no idea what her complete financial obligations are, so don't judge how much money she should spend. I really find it outrageous and wasteful that you would spend $400+ a night on a hotel room, when perfectly adequate rooms could be found for less.
You mentioned that you had an "issue" that resulted in a room comp. Presumably this "issue" caused some kind of discomfort or lesser enjoyment of the room, which is what caused you to get the comp. SIL bore half of the "discomfort" that caused the hotel to comp you. Why should SIL pay full price on that and you take the entire discount? That seems inequitable to me.
I would not be "mad" at SIL, but just know that you and she have different world views and in the future, particularly when it comes to money, it would be better for you to be more explicit about the exact obligations.