Sorry if I missed it, but how old are the gc? Do the normally use car seats or boosters? Because I can see that definitely being an issue, as many kids are in some sort of safety seat until they’re seven (depending on height and weight).
She shouldn’t have raised her voice to you. You shouldn’t have agreed to drive your sister when you’d already made a commitment, imo. If the dr is only 15 minutes away, I’m guessing a cab or Uber would be an option.
As a parent, I’d be upset that my kid missed their gymnastics to sit in a car or dr’s office. That’s not what was agreed to, and to me, doesn’t have the same value as spending the afternoon at grandma’s. I’ve never known a dr to be on time for appointments, and specialist’s even worse, ime.
I also find her being drunk every night to be at extreme odds with her being an excellent mother, organized, etc.