Driving betweetn 12 a.m. and 5 a.m. is crazy. And that's exactly why you won't have to deal with a lot of traffic. People, generally, love their sleep and aren't even THAT concerned about the traffic, but trust, it will make things a hell of a lot easier. The others in the car can sleep, you can do an experiment about whether you react more to three shots of espresso, 50 Cent energy shots, Red Bull mixed with Monster, or ginger shots. When you get to your destination, make sure you get in a quick catnap, let your family wear down the intense relative energy and then go about your day when you wake up.
Just make sure you're driving on Tuesday night/Wednesday morning and not on Wednesday night/Thursday morning. Wednesday is one of the biggest drinking nights of the entire year, and you can bet your turkey-lovin' butt there are going to be a ton of adults "drinking responsibly" at their enormous high school reunions at the local bars. Just because you're smart and know what you're doing doesn't mean the other people on the road do. It's best to just avoid that alltogether.