early in the morning, like 3AM. When my kids were young, this was the standard road trip time. Pack the car at night, get it all ready to go at 3AM, grab the kids from their beds, blankets and all, and strap them in and start driving. You get a good 4+ hours in before they start to wake up, and they wake up pretty happy. Then you stop at a McDonalds or something to eat some breakfast and get the kids dressed, and when you get back on the road you have another 3-4 hours of driving because it's like the trip just started for them. So by lunchtime you can already have driven 500 miles. Take a longer lunch, then drive a couple more hours to your hotel/destination, and use all the DVD's/video games you want then to keep them happy, and then you have a full afternoon/evening for them to be out of the car.