I generally ice them down in a cooler for the ride home when I can't clean them at the lake. (just like I would do the fillets if I did clean them at the lake)
I generally keep them alive in the livewell until I leave & stop and get a bag of ice & put it in the cooler, then take the fish out of the livewell and drop them in the cooler with the bagged ice. The one lake I do this at is 1.5hrs drive back home, and I've done it many times with no spoilage of the fish.