Yoreh Deah Siman 16 Seif 9

 

ט אֵין אִסוּר אוֹתוֹ וְאֶת בְּנוֹ אֶלָּא בִּשְׁחִיטָה בִּלְבַד, שֶׁנֶּאֱמַר: לֹא תִשְׁחֲטוּ אֲבָל אִם נִחַר אֶת הָרִאשׁוֹן, אוֹ נִתְנַבֶּל בְּיָדוֹ, מֻתָּר לִשְׁחֹט הַשֵּׁנִי; לְפִיכָךְ, חֵרֵשׁ שׁוֹטֶה וְקָטָן שֶׁשָּׁחֲטוּ אֶת הָרִאשׁוֹן בֵּינָם לְבֵין עַצְמָם, מֻתָּר לִשְׁחֹט הַשֵּׁנִי אַחֲרֵיהֶם, לְפִי שֶׁרֹב מַעֲשֵׂיהֶם מְקֻלְקָלִים.

 

Seif 9

It is not forbidden to slaughter a mother and her offspring together if they are not ritually slaughtered.

as [Leviticus 22:28] states: “Do not slaughter [an ox or a sheep]3 and its offspring on one day.

However if one decapitates the first one or if it becomes a nevelah in his hand it is allowed allowed to ritually slaughter the second one. If a deaf person, or an imbecile or a child slaughter the first animal alone it is allowed to slaughter the second one, because what these slaughter is not considered slaughtered.