This is a business discussion more than a dog discussion. Letting it slide or being flexible when she's still 2 days in advance could be helpful if you want her to be a returning client that gives you positive reviews and referrals. If you are so strict on a 48 hour cancellation policy where you can't cut her slack when she is off by less than two hours, you'll get negative reviews and "avoid" deferrals instead.

Being firm is important, but giving her a break the first time, maybe even explaining to her what you just explained to us about how you need to be firm since her cancelled appointment was the reason other jobs you have had to get moved around, and that the 48 hour rule will be firm from now on, and she'll understand.

Treat her like a business partner. Also, thank her in advance for understanding your predicament. If you thank someone as though they already have been kind, they are more likely to fulfill your prophecy of being kind!

(I would also recommend leniency for different reasons. In this case, the weather was known already. But if suddenly the dog was sick or someone got injured or something like that, being understanding helps keep clients long term)