Stig's been on a 4 hour ride when I volunteered to be the 'driver' for the day for a rescue. He did really well. I let him out to do his thing everytime I had to stop to get something, which was probably twice. He usually slept or looked out the window. I gave him treats every so often to keep him happy. He was also buckled which I think is a must for long rides.
I'm sure Chester's going to be ok. If you find him getting sick, just make a stop for some fresh air.