Rabbaim: Halachah never states to sit Shiva for a not-Frum child. There was a Minhag for a long time to sit Shiva for a child who intermarried (R’ Schachter says that it was originally only for a son who intermarried and that the Shiva is for his children who won’t be Jewish). Some Yechidim sat Shivah in individual situations to show extreme sadness. From there, somehow, the custom has spread to where a lot of people sit Shivah for a lot of things. But it’s not Halachah.
And there is a Passuk against your attitude. The Torah says, “Lo Yuchal L’vaker Es Ben Ha’ahuva Al P’nei Ben Has’nuah Hab’chor.” The Gemara says that “Has’nuah” means even if he is “S’nuah Lifnei Hamakom”.