Once you pickup your luggage from the luggage claim area, if your bags are big, you probably won't be able to take them back through security to ride the trams. You can always split up and do that.
The hyatt hotel is a very nice a relaxing place. You could maybe pick up a couple of toy planes and go upto the 4th floor, where the restaurant and lounges are. There are alot of seats, and very few people there and it is very quiet and the kids can play while you sit in the big sofas.
If you are renting a car, you could go get the car and put your luggage in and then drive the car out of the rental lot and up to regular parking, may cost around 2-4 dollars but will eat alot of time, and then you wouldn't have to lug your baggage around.
George