Read other letters about this article
While the question of why women sink to cattiness and arguing over men is an important one to ask, there's another one that's probably more relevant in this situation: Why do we women feel we need to make everything okay for everybody? In other words, why do we need to be people pleasers? Why can't we acknowledge our own feelings instead of burying them and focusing on other people's all the time?
Oh, and for God's sake, please don't carpool with her. It's certainly one thing to be civil to this woman in social settings, but it's entirely another to actively put yourself in her path. Don't do that to yourself -- you don't deserve that kind of treatment.