There are paid lounges on the domestic departures level (level 2). 500 yen an hour from memory.
On the international departures level (level 4) there are baggage storage facilities at either end. I think they're still there anyway.
You might want to get on a train and go into Osaka with such a long stay at KIX. Good airport but not much there to keep the big kids from getting restless let alone a 3 year old