So my mum has a few health issues including some cognitive decline (not dementia so far, according to her last assessment) and lives with me and DH. I'm her carer and she's needed more support than usual recently as she recovers from surgery.
Up until now she's always managed to book her own hair appointments from a mobile hairdresser she gets on well with, and I've been happy to let her as it's been one less thing on my (somewhat overfilled, especially as I work F/T) plate!
My mum was ill yesterday and forgot she had an appointment today. (This has never happened before btw.) She was still in bed when the hairdresser turned up, and although she's a little better today she wasn't up to the appointment. Hairdresser was understandably frustrated when I told her this, and I was suitably apologetic, but she spoke to me in a way I'm not at all happy with (especially as I didn't set the fricking appointment in the first place and wasn't aware it was scheduled, which I explained!) 'I've come all the way from [local place about 20 mins away] for this!' really unpleasant tone of voice, no 'sorry to hear she's not well/hope she's soon better', nothing like that. She then proceeded to snap that in future she'd call my mum before her appointments to make sure, then walked out of the house without another word to me, shutting the door unnecessarily hard behind her.
Obviously, this tells me I'm going to need to manage my mum's hair appointments in future, which is OK, but I'm a bit conflicted because in principle I feel we should offer to pay the hairdresser something for her lost time/petrol. BUT, given how rude she was to me, the thought of making this offer is really sticking in my craw atm! 
Part of me genuinely feels bad we wasted her time, another feels that as a business owner this is not the way you speak to a regular and usually reliable client. My mum gets on well with her, she has always been very pleasant and polite until today, and I'm glad of that because my mum doesn't get out much and enjoys having someone to talk to occasionally besides me and DH. So I don't particularly want to look for another hairdresser, but I'm fuming over how I was spoken to over a genuine misunderstanding that wasn't even down to me in the first place! 
WWYD in this situation?
YABU = you wasted the hairdresser's time and should reimburse her
YANBU = why should you do her any favours after she was so rude?