Mishnah Kiddushin
משנה קידושין ד׳ — ד"ה לֹא יִתְיַחֵד אָדָם עִם שְׁתֵּי נָשִׁים
Mishnah Kiddushin 4:12
This mishnah addresses age-related categories in family law and supervision of children, but it is only indirectly related and not a direct source for the permissibility of private tutoring.
לֹא יִתְיַחֵד אָדָם עִם שְׁתֵּי נָשִׁים, אֲבָל אִשָּׁה אַחַת מִתְיַחֶדֶת עִם שְׁנֵי אֲנָשִׁים. רַבִּי שִׁמְעוֹן אוֹמֵר, אַף אִישׁ אֶחָד מִתְיַחֵד עִם שְׁתֵּי נָשִׁים בִּזְמַן שֶׁאִשְׁתּוֹ עִמּוֹ וְיָשֵׁן עִמָּהֶם בְּפֻנְדְּקִי, מִפְּנֵי שֶׁאִשְׁתּוֹ מְשַׁמַּרְתּוֹ. מִתְיַחֵד אָדָם עִם אִמּוֹ וְעִם בִּתּוֹ, וְיָשֵׁן עִמָּהֶם בְּקֵרוּב בָּשָׂר. וְאִם הִגְדִּילוּ, זוֹ יְשֵׁנָה בִכְסוּתָהּ וְזֶה יָשֵׁן בִּכְסוּתוֹ: לֹא יִלְמַד אָדָם רַוָּק סוֹפְרִים, וְלֹא תִלְמַד אִשָּׁה סוֹפְרִים. רַבִּי אֱלִיעֶזֶר אוֹמֵר, אַף מִי שֶׁאֵין לוֹ אִשָּׁה, לֹא יִלְמַד סוֹפְרִים:
A man may not be secluded with two women lest he sin with them, but one woman may be secluded with two men. Rabbi Shimon says: Even one man may be secluded with two women when his wife is with him, and in that situation he may even sleep in the same inn with two women, because his wife guards him from sinning with them. They further said that a man may be secluded with his mother, and with his daughter, and sleep alongside them with bodily contact without clothes, since there is no concern that they will engage in sexual intercourse. And when they, the son or daughter, have grown up, this one sleeps in her garment and that one sleeps in his garment, but they may share a bed. A bachelor may not act as a teacher of children, nor may a woman act as a teacher of children. Rabbi Elazar says: Even one who does not have a wife may not act as a teacher of children.

