You asked for a friends and family discount, and you agreed to pay a third of what you would have paid without the discount. I don't think it's unreasonable for them to expect you to provide accurate information, and I don't think it's unreasonable to call it fraud when the information that got you the great deal wasn't correct -- they don't need to get into why you provided false information. It was your responsibility to be sure of your facts. Obviously, given that this is what I think, I don't think the GM should be reprimanded for accusing you of fraud, although -- I'm assuming here that she was the one who was using a loud voice while you were trying to be discreet -- it might be appropriate for someone to remind her that this kind of conversation really shouldn't turn into a spectacle in front of other guests.

It's just your bad luck that an even better deal came along unexpectedly and you missed out on it because you had negotiated a lower rate by telling them something that wasn't true. I don't think the offer the GM made you was unreasonable, and since you eventually said "Whatever" and walked away, I would consider the offer accepted. I don't think they owe you a refund. I am sure it will come as no surprise to you that I'm not a big fan of the "few free future nights" plan either.

Instead of begging her to call the police, maybe you should have called them and gotten it all straightened out right then. But you didn't. I suspect that even if you had, the police wouldn't have told her that she had to comp your rooms, but at least you'd have had a copy of the police report for when you filed a small claims case.