Correct me if I'm wrong, but Japan does not allow dual citizenship ... rather your children are young enough that they have not had to declare their ultimate citizenship?
My wife and I are naturalized US citizens. My country of origin allows me to retain dual citizenship, as does the US, but my wife was obliged to renounce her Japanese citizenship when she became a US citizen. It's annoying and unfortunate that she had to do so.
Japan does not consider someone an adult capable of making that decision until they are 20. Further, they won't force the decision (nor will the US) even after that point.
This leads to interesting issues. One such individual was in training with me but had to sit and wait 6 months until he turned 20 to renounce his Japanese citizenship so that he could obtain a clearance. This was 20 years ago, so things may have changed.
My wife and I are naturalized US citizens. My country of origin allows me to retain dual citizenship, as does the US, but my wife was obliged to renounce her Japanese citizenship when she became a US citizen. It's annoying and unfortunate that she had to do so.