Faced with those alternatives, if it were I, I would find a piece or more of eggcrate foam ( alternative: numerous layers of folded bath towels?)to cushion road bumps and plug the bator into the car and set it on the floor on the foam. By tomorrow AM, there may be chicks or there may not. I would not worry about opening the bator to stop the egg rolling especially since you have pips. Hatched chicks will roll other eggs by themselves. Concentrate on keeping the bator steady and heated.
Keep your mind on your driving and check on the bator during breaks. I'd bring some water in a spray bottle to add humidity if something strange happens: lid pops off or something like that.
When you get where you are going, set up the bator gently and hopefully all will be fine. You do not have to open the bator for at least 24 hours after the first chick hatches. Of course, many of us do
I go thru my LG's windows to remove rambunctious chicks and let the others hatch.
Find a fairly large box for your destination and rolls of paper towels to use under the chicks. You don't need the mess of shavings if it will only be a few days.
Make sure you have chick feed and a chick waterer with you and of course, the heat light.
For the return trip, I'd use a smaller box for the chicks and scatter food on the bottom every hour or so, and stop to offer water to them every hour or so. IMHO, leaving water with them during the trip will just lead to mess. Just stop and offer water regularly. If you travel at night, I wouldn't bother to stop because chickens don't eat during the night when it's dark. For heat during travel, I'd go by the noise of the chicks. It's possible that the body heat of them in the closed box will be sufficient to keep them happy. Dont' crank the air conditioning up high! If they are noisy, it means something is wrong and you need to figure it out.
Sorta like a new baby... they cry and you figure out why!