First, I would indeed talk to the superintendent about one of his/her employees getting involved with private matters. It doesn't matter if you had a disagreement about what the weather would be like tomorrow, if the teacher chastises you for your part in a private matter (especially if they allude that the other parent spends more time with the class, and therefore must be right) then they have overstepped their professional bounds. (by the by, if you absolutely have to talk about what the disagreement was about, I recommend saying "my pet" instead of "my snake")
Regarding the comments she made about snapping a snakes neck, being civil is usually the way to go. Let this woman know that your snakes are important to you, and that her comments are hurtful and rude. You wouldn't threaten to kick someones dog? To smash their private belongings? It isn't appropriate to threaten someones property, and this woman seems to need to be reminded of that (weird, yes, but some people don't think of anything scaly as a pet and need to be reminded that they are).
If your kids are friends, try to keep things as polite and civil as possible. What will your son do when his friend comes and says he isn't allowed to talk to him and he has to change classes now? Be calm, even though we all know by now you must be itching to slap this woman.