The current term "code-switching" is what many people seem to do when faced with social groups in which different languages are spoken.
When I was teaching (in urban public schools) we used to call what we taught in school as "school English" or "job English." We made the point that it was important to learn, and we tried to do what you seem to be doing: not put down the language as it is spoken in the home or outside of school.
As a teacher, it took some time to get used to some of the terminology. I remember sitting at my desk, writing something, when one of my third-graders came up to me and said, "I gotta use it."
The only thing I could think of that the "it" referred to was the pen that was in my hand. As I handed over my pen to the student, I told her, It would be better if you said, "May I please use your pen?"
She was, of course, not interested in using my pen!!!!