I have flown with JAL and pets in the cargo hold before, just with dogs, not cats. JAL has a very good reputation as far as treatment of animals entrusted to them is concerned, and on my half-dozen flights with them everything went well.
Are you talking about
checking your cats in as baggage with JAL or having them fly
as manifested cargo with JAL cargo? And when are you planning to fly?
If you plan on checking them in as baggage, as far as I`m aware, Japan Airlines currently has suspended JL 67/68 and only plans to restart nonstop service to Seattle in March - and these plans may change depending on the covid situation. If you plan on flying before that date, you'd have to connect to either Alaska or AA, which means you need to book the cats separately on either airline, pay separately for the intra-US segment and comply with all relevant rules.
The only airline flying this route and allowing cats in the cabin is
Delta. I don't know if your child will be able to book a pet carrier if in their own seat, if yes you can bring all three of them along.