I would bet good money that you haven't been told the whole story. Allergies are a common reason given when trying to rehome a dog but not wanting to give the whole story. It's amazing how many children develop allergies when dogs are in the arsy teenage stage...
I would be wanting to do all of the following
a) meet the dog in the home. See evidence that the dog really does live there - dog hairs in the crevices, toys lying around, dog has an evident bond with the owners, interacts appropriately with the non allergic first child. Keep an eye out for signs that the dog is destructive eg chewed chair legs or scratches on doors.
b) ask the owners to demonstrate the skills the dog has - you don't need competition obedience, but if the dog doesn't know its own name or can't manage a sit / down / paw then it's a sign it's completely untrained and you'll have a lot of work to do. Don't assume it's house trained; in any case, accidents are common in new homes.
c) take the dog out for a long walk, ensuring that the dog meets the most common triggers (eg strangers, other dogs, traffic); I wouldn't take a dog that reacts badly to these as from bitter experience it's somewhere between difficult and impossible to fix, and eternally stressful. Does the dog pull on the lead, is it allowed off lead, does it come when called? This wouldn't worry me too much as it can be taught, but it's part of the overall picture.
d) have the dog independently assessed by an APBC or CCAB behaviourist, or APDT trainer. They will be able to spot things that you cannot.
e) speak to the vet directly, and get copies of all medical records. In addition, get a check up to make sure there are no problems that have been missed / ignored. Get the chip checked at the same time.
f) find out why the dog isn't being returned to the breeder or rescue - good ones have a clause stipulating that the dog must be returned to them in these circumstances. Also be aware that KC certificates don't mean the dog came from a good breeder - it just means the dog is purebred, but the certificates are routinely faked anyway. Know the difference between the breed register and the activity register (the latter of which any old mutt is eligible for).
g) take the dog home for a three day trial (being aware that this is a honeymoon period, but hopefully any massive issues will become evident during that time).
I adopted a dog privately, and while I adore him, he did come with a few surprises. The first time I met him (on a house viewing for a flatshare) he appeared to be a sweet but energetic young thing with no issues. When I moved in it rapidly became evident that he was totally untrained apart from being house trained. When I started walking him I discovered the behavioural issues. 6 months later when I formally adopted him, I still got some surprises (eg microchip registered to unknown third party, vaccinations not up to date, possible health problem actually hadn't been checked by a vet...). Had his well meaning but totally clueless previous owner been asked to describe him, he wouldn't have been able to articulate his issues because he didn't recognise them. I have dealt with the problems because I had no choice, but it has been hard and he'll never be the perfect dog. I've also adopted small furries (where much less can go wrong!) from strangers and I've never yet got there and found the animal as advertised - including one where the picture showed a different species to the animal I was actually handed!