The simpler, cheaper, and IMO more elegant solution is to run what is know as "thin client" software. It essentially allows you to turn 1 computer's hardware into multiple computers.
Now, in a CarPC environment, this does run into problems with multiple audio sources/signals and only 1 sound system (though I guess you could go for multi-zone audio if you felt like making it complicated). The only solution I've come up with is to get yourself a cheap set of RF wireless headphones for each user.
ThinSoft makes thin client software, and also a combined software/hardware solution that I believe is probably the perfect thing for what you are looking to do. It's called the Buddy B-680 Premium.
It includes a USB/audio hub with a separate audio output for the thin client and a 4 port USB hub for devices that will be associated with the client (The thin client can still access the USB devices on the main PC) and a PCI VGA video card to output the thin client's video.
The thin client acts as it's own fully independent computer, capable of doing everything the main PC can do.
I was brainstorming the other day on how I would do a multi-user CarPC setup if I were to attempt it (still deciding on it in my next truck, it'd be really cool but I have no use for it, being single and not really caring about my friends' ability to enjoy MY CarPC ) and this is what I would come up with.
I would order 2 7" touchscreens, install them in the headrests, get 2 of those Buddy Premium kits, and if I wanted to get really crazy, wire each of them up with a Space Navigator in their cupholder and a slot-load DVD in the back of the center console. Then I would buy a cheap 3-channel RF audio wireless headphone setup, enabling each user to listen to either their audio, the other backseat passenger's audio or the main PC's audio simply by flipping a switch on their headphones.
Then, each passenger could enjoy their own independent front-end software, audio, movies, games, internet, whatever, without nagging me about not liking my music.
Though I did the math and I realized the cool functionality probably wouldn't be worth the extra $1200 to make it happen In your case, where you are looking at adding whole separate PC's for the kids and with you having to purchase the touchscreens anyways, the cost savings of the Buddy system are significant.
However, depending on what you kids are doing with their thin clients, it can probably be a drain on your main PC's resources, so you might want to take some of the savings and invest in some more RAM and processing power.