The night before you leave, box up the dragons in either cat carriers, or rubbermaid containers. Don't include any lights etc in the boxes. They will sleep in the box over night and during the drive. In the hotel room or wherever you plan to stay over night, you can take them out of the box and let them bask and give them water only. Pack up before going to bed so they are ready to leave the next day. Once at your final destination, set up their cages and put them into it, give them a few hours to heat up and offer food then.
Healthy adult dragons can go 2-3 days without food without any problems. Hatchlings or dragons under a year old shouldn't be kept long without food, 24 hours should be fine.
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PHLdyPayne