Our Gemara on Amud Beis discusses why they did not teach cheder children new pieces of Torah on Shabbos.

אֶלָּא: גַּבֵּי שַׁבָּת הַיְינוּ טַעְמָא דְּאֵין קוֹרְאִין בַּתְּחִילָּה — מִשּׁוּם דְּיִפְנוּ אֲבָהָתְהוֹן דְּיָנוֹקֵי לְמִצְוְתָא דְשַׁבְּתָא. וְאִיבָּעֵית אֵימָא: מִשּׁוּם דִּבְשַׁבְּתָא אָכְלִין וְשָׁתִין וְיַקִּיר עֲלֵיהוֹן עָלְמָא. כִּדְאָמַר שְׁמוּאֵל: שִׁינּוּי וֶסֶת תְּחִילַּת חוֹלִי מֵעַיִים.

Rather, with regard to Shabbos, this is the reason that children may not read a passage in the Bible for the first time on Shabbos, so that the fathers of the children will be at leisure to fulfill the mitzvah of delighting in Shabbos. Teaching new material to their children would occupy more of their fathers’ time, limiting their opportunity to fulfill that mitzvah. And if you wish, say instead: Due to the fact that on Shabbos children eat and drink more than they are accustomed to eating, their world is heavy upon them, i.e., their head and their limbs are sluggish, and they are incapable of concentrating and studying well, as Shmuel said: A change in routine [veset] in eating and the like causes the onset of an intestinal ailment.

One way or the other, we see our sages were sensitive to child nature and their ability to tolerate new studies on Shabbos, and how it would impact them, or their parents' mood.

Reflecting on this, we must consider what happens at a family table.  All that is good or bad in a family can occur because there are no distractions of work or phones, and the expectations, pressures and intimacy all come together.  So in dysfunctional families, Shabbos tables are nightmares of aggression and out of control behavior, and in functioning families, wonderful times of connection.

Consider that parents have about 1,000 shabbosim (52 a year for about 20 years) to impress upon children the mesorah, holiness of Shabbos, the basics of faith and halakha, and the joy of mitzvos.  That is not a lot of opportunity. Do not waste a single Shabbos. Make sure your table is happy and joyous and that each child is able to learn and experience what they can, given their personality, strengths and weaknesses.