@Maureen89 Oh dear - You seem to be confirming the suspicion that helping guests by being accommodating of their needs then just backfires as they make ridiculous requests.
Sadly, unless the guest has reviewed you, you will most likely get a bad review whatever you do.
Have you reviewed the guest? If you haven't then perhaps, if true, 'XX was a lovely guest whom we helped out with pet accommodation and an early check in only to be rewarded by a refund claim post stay due to an overnight power outage out of our control"
For the future I would add into your listing something like "As we are in a rural forested area we occasionally get power outages but have a gas stove/fireplace to ensure guests are kept warm and fed"
Now what to do...I think I would say no to any refund and risk a bad review. Perhaps explain that if the outage had affected her smooch you would have allowed her to terminate her stay but that as she didn't request this you are not willing to do anything in retrospect. Then be ready for the bad review - Any comment you leave to mitigate it MUST be addressed to future guests NOT the person who left the review. something like 'I was disappointed to get this review but expected it as we refused a request for refund when the power went out overnight. Had the power outage truly affected the stay we would have offered to allow a cancellation with a suitable refund.'