No we don't. We only know that she knows more than we know she knows, which is already way more than Nanase know she knows.
... that makes sense. I mean, I still think Mrs. Kitsune don't like her daughter hunting monsters, but yes, it's entirely possible she realized she can't do anything against that ... she DID sent her to the school Raven teaches in, after all ...
It was SUSAN who was sent there couple years earlier. Nanase actually known enough french to go there without parent intervention.
You forgot to mention one assumption you are making: that she wasn't aware that there are magic-users who are actively hunting her daughter BEFORE. Despite her "I don't have a sister", she knows much more about Noriko than we do.
... maybe her reaction to Ellen dating her daughter would be worse if Ellen wouldn't be magic user. She likely tried to keep her away from Tedd before, but now she seem to gave up that plan and might be scheming to empower the Main Eight ...
(About the "aware of her friends being magic-users" ... well, even if not directly told, she likely could realize what Greg's training is doing. So we can assume she knows about Elliot, Ellen and Justin being magic-users or on the way to becoming them, and she likely knows about Susan. Not sure what she thinks about Tedd. Not sure if she knows Sarah and Grace at all - she may not even know about them being Nanase's friends - wait. She gave Nanase the task of helping Tedd courting Grace.)