I suggest you replace "stern" with "civil," "matter-of-fact," or even "business-like."
You DON'T have to be (nor should you be) a DIKK to her. You just don't have to kiss her azz, either. Just do what's right for you and your daughter -- The Right Thing To Do -- and however your wife chooses to respond to that is not your concern.
Once you learn to master this skill (and it IS a learned skill), I think you'll find it amazingly liberating.