Many good suggestions here --
Traveling with a cat is different for everyone. Since this cat doesn't "know" you, it will be a challenge for all of you.
Cats will run faster than you ever think possible so I would never let them out of the carrier...sorry others will disagree. If you are in the front and they are under the back seat or under one of the front seats, you cannot reach them without opening a door and then the cat is outta there. If the cat "knew" you and trusted you completely then it would be your choice to let them roam.
Generally a vet will give you a sedative for the cat to ease it's discomfort. Be aware though it may still meow just out of instinct. Ours did NOT like having the radio on...I think the high pitch was too much for them in the car.
Most cats sleep all day so to be in the carrier is not a problem. Still have a harness on them. HAVE the leash ATTACHED at all times and hooked to the outside of the carrier. Should the carrier come open or they slip away while putting them in it...they will be tied to the carrier.
Take some "old" litter with you to use. It will smell like them already and won't seem so strange. BE sure to use their normal litter box if possible.
Don't put food in the carrier...again they generally sleep all day. Feed them at night and a little bit in the morning to avoid them getting carsick. A couple days of light food will not hurt them by any means.
Think about having "treats" for them to nibble on.
Take a few bottles of the water they are used to drinking with you. Strange water can also give them a tummy ache. Be sure to give the bottles to your son to use also for a few days.
Keeping their vision limited may also help with them being happy.
Think about getting it micro-chipped as a gift to your son if it isn't already...as a "just in case".
Always err on the side of extreme caution. It would not be a good experience if something happened to it.