Transit Guam

Coming from Europe/Hongkong with a jetlag, we will arrive in Guam at 6 a.m. and continue our trip for Yap at 10.35 p.m (same day). Since we will travel with children I'm just wondering if there is some kind of relaxation room at the airport of Guam or if there is an other opportunity to get some sleep...

I don't think that there is. That is a looong layover. I would suggest a hotel- perhaps one with a pool. Get some sleep, take a dip in the pool, get some more sleep- and you will all enjoy the rest of your trip far more.