Matters Subject to Halachic Dispute[1]
In any matter of Jewish law where there is a dispute among halachic authorities as to whether an act is permitted or prohibited, and some authorities permit it even Lechatchila, then it is permitted to instruct a child, even one’s own child, to perform such an act, even if the child has already reached the age of chinuch. [Nonetheless, it is customary and praiseworthy that parents, where possible, accustom their children to follow the more stringent rulings (lechatchilah) and to act stringently in matters of halachic dispute. This practice reflects the traditional approach to chinuch and a desire to train children toward higher standards of observance. That said, in specific circumstances many are lenient, particularly in commonly encountered cases such as opening bottle caps on Shabbos, opening a refrigerator door when the motor may turn on[2], and similar situations. In such cases, reliance on the lenient opinions is widespread.]
Likewise, it is permitted for a child to perform melachah on one’s behalf after nightfall of the Geonim’s time, even if the person himself follows the later time based on Rabbeinu Tam. Since this too is a matter of halachic dispute, one may rely on the lenient position with respect to instructing or benefiting from the actions of a child.
[1] See Rama 259:7; Admur 259:7; Beis Yosef 269; M”A 269:1; Makor Chaim of Chavos Yair 259; Ateres Tzevi 259:6; Piskeiy Teshuvos 343:3; 8; 259:2; See Toras Hakatan [Rubinovitch] Chapter 2:29
[2] See Az Nidbaru 8:23