Hi A.,
Well, my take is that it sounds like a seriously stressful situation, dropping the kids off at school. Nerves were likely frayed on both sides. While your comment was kind of aggressive, her reaction was totally nuts-- she should be ashamed of herself. I mean, you did NOT deserve a reaction like that. In hindsight, if I were you I probably would have just closed the door, with or without a comment to her.
I know how you feel tho. The other day I was at the library with my two kids. I went to the self-checkout station and put my stuff on the counter, while trying to check out the books and keep an eye on a toddler and a preschooler who have a tendency to run around and be loud, and it is a library. Anyway, some lady came up next to me with her books. I didn't realize there were two check-out computers; I thought one was a search computer. She says (mildly aggressively I thought) "Which one are you on?" I said snidely, "The one that checks out books." She said, "They both do." Honestly, I thought it was pretty obvious that the one I was standing in front of was the one I wanted to use, but my books were piled between the computers, so that was apparently her beef with me. "I said, oh sorry." and I raised my eyebrows in such a way that she realized what she had done and was extra-smiley with a "no problem". But to me the whole scene felt passive-aggressive. I wish I would have handled it differently, i.e. laughed it off, lightened the mood, let her off the hook by not acting so pissed off. I felt like I was very rude and I'm not pleased with my behavior. But it is what it is. I was trying to deal with my kids and check out our books and here this lady came and acted like I was a selfish person hogging the whole station. She couldn't step in and do her thing (there was room) or just wait a nanosecond until I was done. But now I'm sure we both feel bad about it.
I know this is not nearly as dramatic as your situation, but I totally understand how you feel, and the reaction you got from her was completely unwarranted. If you want to feel better about it, you might be able to catch her another morning and offer the olive branch, but I don't know what kind of a reaction you will get. I don't know if you are even interested in that given the insults she threw at you. Good news is, in time your emotional reaction to this memory will fade and it won't get you so stirred up. Venting about it should help, so vent away! It's a really crummy situation and I hope it fades for you soon.