In 2007 I moved from NJ to AZ in August. I rented an RV and drove for days with over 50 adults, 20 or so babies and and two clutches in the incubator. Everything made it fine. I bagged the adults up and packed them like I was shipping them. I put babies in deli cups with aspen. I actually pinned my incubator on a seat in the RV. I would plug the incubator in at night when we stopped and threw a few heat packs in there when we were driving. The incubator would drop into the low 80s but I hatched a clutch mid way and one hatched about a month later. No issues at all. The RV rattled like you wouldn't believe. I was about a half hour into the trip and figured I'd lose the eggs for sure. I brought ice packs just in case and everyone made it fine.
This was a significant trip but yours sounds pretty small, you'll be fine with some planning.