I would recommend JL's program - JMB.
Their awards on JL metal are the best all-around option between US-Japan, with economy starting at 27k one-way. Given how JL econ is one of the best products around, it's a pretty good deal.
Their miles expire 3 yrs after earning, but perhaps you will have accrued enough for a family trip by then. Consider getting the JAL credit card for US residents as well.