Normally, I'd say don't worry about the pig infecting your kids, but since your two have immune system problems, you need to be a little more careful.
Viral infections generally don't jump between species. If you followed all the media coverage of the H1N1 virus, you know that it happens rarely. But bacterial and fungal infections can spread between any two warm (and some cold) blooded animals.
Sneezing in guinea pigs can be the result of a respiratory problem, dusty hay or bedding, or allergies. Generally, a respiratory problem will also present with runny eyes and/or nose, and there'll be quite a bit of sneezing. And if your pig has bordatella, he'd likely be looking very sick, puffed up, not eating, and possibly dead since you got him -- it usually moves very fast. So I don't think that's it.
Sneezing due to dust seems to occur most often when the pig has had its nose in the hay, or has been running around the cage and stirred things up. Sneezing due to allergies usually follows a pattern of feeding (allergy to hay is probably more common than allergy to vegetables) or other exposure to the allergen (the cleaning solution used for the cage, or the detergent used to wash piggy laundry, or something you spray in your house, or whatever).
In your case, if you're housing him on something that can have dust (e.g., not on fleece), or if the hay seems dusty, I'd change those things and see what happens.
Where did you get him? If you bought him from a pet store, he may well be ill -- they're notorious for selling sick pigs. But if so, please don't take him back to their vet -- find your own exotic vet, get him treated, and present them with the bills.
What kind of bedding is he on? If you have pigloos in the cage, please either take them out or cut another door in them -- there's no air circulation in them, and the pig breathes the fumes from its own wastes. All hideys should have both an entrance and an exit. Dollar store step stools make great hideys.
