I'm mad at my sister for wanting to get food after we've already left
Was it really a bother to you to get back and get some food?
I would be mad because I left my dog and this is something my dog and I never do.
Rather than going back to your place to get food and mess up your dogs schedule, why not compromise and get your sister a snack to eat while you're out? Being mad at her for being hungry isn't the healthiest end to the situation.
Fuck it, I'm not going back...
Make sure you tell her exactly that. Be firm and not change your mind about getting back to get food.