I need some advice, and I'm not sure I'm equipped to figure out things, and I think I'm actually in fact unable to do what I want.

I'm flying with my wife and son (10 years old) from the US to HND later this week on AA metal. We land at 5-6am and have a JAL domestic flight at noon. I'm OWE, but with 3 passengers, I can only get one guest into the lounge. On previous trips with my family out of Haneda, we've been able to get everyone into the HND business lounge, even the three of us due to reciprocal Admirals Club benefit. However, I just read, that only works with a same-day departure on AA metal, which we won't have, only same-day arrival.

Furthermore, we're going to the domestic terminal, so I doubt the JAL/OW lounges there are giving any reciprocal benefit. Given my son's age, I don't think I can/should rotate guests in and out of the lounge since I have to be present the entire time. Leaving my son alone in the terminal in another country seems a bit irresponsible, even though he's mature beyond his years and has a phone.

Any ideas? Is there a paid lounge on the domestic side my wife can use, ideally to shower while I take my son to the OW lounge? Is there any other option I'm missing here using OWE or Admirals Club. I'm sure this is worthless, but our domestic ticket is NOT interlined and is booked directly with JAL in J class (HND-ITM).