Indeed, there's a place for ...דוחה שמאל sometimes we must correct our children. We can't allow them to do whatever comes to their minds. But the דוחה שמאל belongs to the rest of the days of the week. On Shabbos, we must only conduct ourselves with מקרבת ימין.
If a person is mechanech his children on Shabbos in a manner of שמאל דוחה, with sternness and strictness, he should yell at himself, Nu! Shabbos! This is not the time for this! "But it is my responsibility," he will say. No, on Shabbos this is not your responsibility. The Shabbos concept of עשויה מלאכתך כל כאילו, as if all your work is done, applies to the area of chinuch as well. It's all taken care of, and Shabbos is not a time for correcting and educating—but a time for peace, love, and closeness.