Note that the individual in the linked article is different from your family's case because she naturalized as a US citizen.

Japan seems to enforce loss of citizenship more strictly in these cases. If your children are dual citizens from birth, different laws apply. As an example, despite Naomi Osaka publicly declaring to choose Japanese citizenship, she has not been reported to appear in the US government's "Quarterly Publication of Individuals, Who Have Chosen to Expatriate". [1] [2]

[1] https://www.ubitennis.net/2020/12/naomi-osaka-and-a-tale-of-... [2] https://old.reddit.com/r/japan/comments/16i22mh/dual_citizen...