Unless I'm reading it incorrectly, it sounds like OP is a party of four consisting of two adults and two children. I interpreted it as OP heading out and the second adult staying behind with the two children.

FWIW, I had a similar layover a few years back as a solo traveller (TG BKK-HND to NH HND-CTS) and I ended up at the Hotel JAL City Haneda, which is down the street from the Keikyu EX Inn Haneda. The area around the hotel isn't much to write home about (main attraction: the Yamato Group's Chronogate facility, which does offer tours) but there are a few restaurants, konbini, etc. Sadly, I don't have any recommendations for food as I'm pretty sure I just ate sandwiches I purchased from the konbini. The area was certainly nothing exciting but it was sufficient for an overnight layover and wasn't difficult to get to via the Keikyu Airport Line.