Hi KathyMoore,
Continental Micronesia operates the flight you are talking about, it's called the island hopper. Flights 956 and 957 are both Boeing 737-800. One goes from HNL to Guam (957) the other goes Guam to Honolulu (956), and they alternate directions each day. And both cross the international date line. The new 737-800's (with increased FC seats) are not in service out here yet.
It's a killer flight made worse now due to FAA regulations that require half the plane to get off at each stop with all luggage. They pick sides, say seats ABC, or DEF, and if you are in those seats you have to get your bags and get off. The other side that is allowed to stay on the plane has to get their carry on and put it in their lap, then switch sides while they inspect the aircraft. FSM is currently trying to work with them to change this rule but as of right now it is out of their hands.
HNL to Majuro (Marshall Islands) to Kwajalein (military base not allowed off aircraft) to Kosrae to Pohnpei, to Chuuk to Guam. And of course it can be nice to get off the plane.
You will go through immigration control at GUAM upon entering, and then upon return to HNL you will go through immigration control. Entering HNL from the mainland there is no immigration control.