Shabbos Violator

The Gemara in Eruvin (69a) tells of a man who would walk in public areas on Shabbos, clearly wearing an item that is considered a burden. In other words, he would consistently publicly carry on Shabbos. However, whenever he saw R. Yehudah Nesi'ah, he would cover the item. Because of this, the Gemara concludes that he is not considered a mumar, the status normally reserved for public violators of the Sabbath. R. Avraham Hayim Schorr, in his Toras Hayim (ad loc.), suggests that one can infer from this passage that any person who publicly violates Shabbos but has at least one person before whom, out of respect (or embarrassment), he refrains from such violation, then this person does not have the status of a public violator of Shabbos. This ruling, if accepted, has tremendous implications. As stated above, a public violator of Shabbos (absent other considerations) has the status of a mumar le-khol ha-Torah and is treated, in regard to many laws, as a gentile. However, if such a non-observant person refrains from Shabbos violation when in the presence of a respected rabbi or a beloved relatived then the status of mumar does not apply.

I saw in the footnotes to the book Shulhan Shlomo (on Orah Hayim, 512), that someone asked R. Shlomo Zalman Auerbach whether he may invite his non-observant son for a Yom Tov meal. Since one is not allowed to cook on a holiday for someone who does not observe Shabbos, may one invite one's non-observant child? R. Auerbach responded that since the son will not violate Shabbos in front of the parent, the man lacks the status of mumar and one may cook for him on Yom Tov.

(As always, consult your rabbi before applying this.)