This is kind of ridiculous.
JAL basically can not serve as law enforce and deny boarding for someone who has valid travel documents.
So there is the line? Who does not the US dad sue the following people?
1) Company who supply the jet fuel to JAL
2) Public transportation company or relatives that transported the mom and children from where they live to the airport
3) Public transportation company or relatives that picked the mom and children from Japan airport
4) USCIS at the gate since they did not stop the mom and children boarding
5) Airport. If there is no airport, they won't get away
6) Department of Transportation of CA. If there is no road or highway, it will be very difficult for them to get to the airport
7) ....

For this case, the dad has the custody. Mom was breaking the US law to take the children aboard. But suing JAL is too much. The dad better gets another lawyer.