Joy, your DS and DDIL may want to consider possible ways to reduce allergens in their environment, if they can, to mitigate the allergens that a new pet might introduce. For instance, carpeting is terrible for allergies. You can never get it completely clean, or keep it completely clean. For that reason, I choose to live in homes with hardwood floors or tile intead of carpeting. (I do have a couple of oriental rugs, but that's all.) So...if your DS and his family happen to fall in love with a shaggy, hairy, allergen covered beastie, there may be ways to even out the negatives and still welcome the dog into their lives.
BTW, I believe they have discovered that children who grow up around animals tend to develop fewer allergies as they mature. I'm not suggesting that they shouldn't take allergies seriously, especially if your DDIL has strong allergic reactions. But sometimes the answer to a problem seems counter intuitive at first, you know?
Also, if they go through a rescue organization that fosters dogs, they may be able to take a potential candidate home with them for a few days on a trial basis before making a final decision. This may be a way for your DDIL to find a dog that is less likely to trigger her allergies. This would be far less traumatic than buying or adopting a dog outright, and then finding out later that the allergic reaction is too strong. Then, they would have to return the dog, if that's even allowed, or rehome the dog themselves. In a foster situation, the dog would go right back to where it has been living with far less stress on the pet and on your family.
Also...and this is just my personal experience...I have a very strong allergic reaction to cats. If I touch them without medicating myself first (and how can I not touch them, assuming they will let me?) my eyes quickly become so puffy that they will almost swell shut. *However*....if I actually live with a cat, the allergic reaction tapers off over about 4-7 days until I no longer react at all to that particular cat. I find it weird, but reassuring. Someday, I may be able to share my home with a cat (or three) again. Right now, my dog wouldn't allow it.
After all that, I'm going to go read the article now.