Most definately, yes, let the porters that are there to help with your bags, take them from you. No need to try to lug all that luggage, plus keep track of your teens and carry on bags. Just tip the porters a buck or 2 per bag and you and your kids just handle the carry-on's.
They will let you carry luggage onto the ship but it must be able to fit through the same x-ray thing as the airport. We usually carry all of ours on and it was a tight fit the last time but it worked. Best advice pack light wash a few things by hand or send it out to be cleaned.