Am I doing the right thing?

A friend of mine suffers from depression. As a result, she tends to get unreasonably emotional over small things. Well, she doesn’t have a car, and she called me asking if I would give her and her four-year-old son a ride home from his school because it’s “so cold” out. Well, it’s about 25 degrees, which is not that cold if you’re dressed right (kids will play outside in the snow in this weather for hours,) plus it’s only about 5 – 10 minute walk to her house from the school. That’s REALLY not a big deal. It’s not like it’s 4 degrees or something.
Anyway, I initially said yes, I’d give them a ride. Then, during this same conversation we had a small misunderstanding. Instead of just conceding, as I did, that we had had a SMALL misunderstanding (it was very brief, and there was no yelling or anything,) she proceeded to hang up on me.
She calls me to ask a favor…and ends the conversation by rudely hanging up on me.
I called her back, left a VM that said, “Um. Excuse me. You just hung up on me. Looks like you guys are going to need to find another ride, or walk.”
Well, it’s the time I was supposed to pick her up….and I’m feeling guilty, but forcing myself to just sit.
Did I do the wrong thing?
I know from experience that he behavior will change for the better accordingly, that it’ll be a while before she acts like that again so…..?