They all react a bit differently to road trips. It might be a good idea to take them on a short car ride around town to see how they respond. That said, all of my guys have been great on road trips. I brought my current dragon on a road trip from Iowa to New Hampshire and back this summer and he did really well.
I'd keep them on leashes in the car so they don't get underfoot if they roam around and get squirmy. It's helpful to have someone else in the car to monitor/manage them if you can. I keep a soccer style duffel bag in the car for transport. I have a fleece blanket at the bottom and carry hand warmers to put under the blanket if I stop for food and leave the car for long but only use them in the winter. Summer car temps are OK but if you leave the car, leave the windows down a bit so they don't overheat. Give them some rest stop breaks to sit on a bench and bask in sunlight a few times per day and that should cover lighting. I keep a ziploc with a square of paper towel to hold salads and a container of black soldier fly larvae for meal time. You'll want a bag with cleaning supplies in case of accidents too.
They can sleep in their duffel bag (or cat carrier, or big shoebox, etc) in a hotel along the way. I have a clamp lamp basking light that I hook up (it has a mercury vapor bulb but a regular halogen flood light is fine) in the mornings for basking and breakfast time. The big foldable baby play pens work well if you need to contain them in a room. They are much easier to manage than a tank.
It sounds like a lot as I write it, but it's really not a big deal if you already have a routine down for them. You just need to adjust the routine a bit to make it mobile.