Wives overreact. That's what they do. (Husbands too, a lot of times).
If you make this a big deal by arguing too much, it's going to become a bigger issue, though. Whatever insecurities your wife might have will be made worse by you "taking sides" with the other woman.
I think it's best to just try to ignore it, and reassure your wife.
EDIT: Just saw your post above. I don't agree with cutting off all contact. It sounds like that would just hurt this woman's kid.
Also, I don't love the idea of your wife going through your texts. I know you've got nothing to hide, but on principle, it's a bad sign. Insecurity is a natural thing, but when it starts reaching a certain level and is impacting other peoples' lives, it's fair to call it "overreacting".
I think you probably need to have a conversation about her jealousy, and I do think it's important to reassure her that you're the only one for her.
I'm lucky. My wife is only insecure of the blog.

EDIT 2: wdleehi's suggestion below is a good one. If you guys still do the carpooling, but let your wife handle the contact, it's a win-win.