"Honey, what are THOSE doors? Are they emergency exits? Does the school allow students to use those doors for normal exit? Wouldn't it nice if you could use those doors in a weather like this?"
You made an assumption, you know about the school better than she does. She thinks it is a dumb idea that she goes off this way while everybody else are going the other way.
You may have waited all day long to have someone to talk to, but she craves some quiet time after all day's work. Next time after she gets into the car, say hey and stay quiet until she says something.
You may be the type of person who searches for validation, self worth, or even your very existence, in the way others react to you. They are like walking mirrows through which you see yourself. Their approval are the stuff you feed on.
Why all the struggle and commotion? You know you are a good mother the kids are fortunate to have.
Time to think about your own life. The kids may find something interesting there.