First and foremost, applause to you for tha loyalty to your other half. But if it's just you and tha wifey with no kids, then yes she's overreacting. But this is also (which i'm sure you know already) just women being women. What "totally freaking out" means, I don't know but as long as she isn't throwing pots, pans, and knives, you're fine.
If this wasn't a group message to tha fathers she may know, it still just may be a nice harmless acknowledgment. I must say tho all connects in this friendship (for tha most part) should only run through your wife and this woman to avoid stuff like this. Little things like this can turn into something unnecessary. Again this is women being women and tha fact this other girl is single doesn't make this easier to explain or smooth over. Just try not to be a "DB" and look at it from her side. Though we aren't emotional as women are, how would you feel if this was a man telling tha wifey Happy Mothers Day.