I mentioned your daughter as you'd originally said you had taken a pup from her. It sounded like this was the same dog, but thank you for clarifying.
Because we do not know what type of dewormer has been given to the mother (but you did say that hookworm treatment is given 2 times a year), I would first be concerned that the puppies (not just the one with dark stool) may well have picked up intestinal parasites along the way. If the mother has them, the babies are likely to acquire them through her milk. Worms can also be acquired from their environment, though they're a little too young for this to be likely. Hookworms and roundworms are the most common when we consider those that young puppies may have. Most veterinarians recommend deworming puppies early, even as early as 2 weeks, because of the risk involved. Hookworms are typically to blame when we see diarrhea and suspect intestinal bleeding (which can result in a dark, tarry appearance to the stool). In many cases, once one puppy begins having symptoms, the others will then start having symptoms. The time line is right for hookworms to be the cause here. I would recommend taking a sample of stool in to your vet's office to have it checked, but no matter the outcome deworming is still recommended. In about 33% of the cases, a fecal may show a negative result but intestinal parasites still be present.
There are other parasites and protozoan that are common in puppies and this link discusses them at length:
http://www.carnivora.ca/html/learning_centre/parasites/index.cfm However, without a doubt, hookworms are the most common in puppies with the symptoms that you mention.
Your vet is likely to recommend a deworming regimen. One of the most common medications dispensed for this is pyrantel. You can purchase medications like this without a prescription and dosing information comes with the bottle: http://www.revivalanimal.com/Pyrantel-50mg.html?feed=BingShopping Your vet will need to dispense a syringe for dosing for you and may recommend a different deworming schedule for the puppies and the mother. Alternately, you can also purchase pyrantel from your vet, in a smaller quantity and there will be no lag time for shipment and dosing. Hookworms can be a death sentence for little ones like the puppy having issues. In some cases, they can pass away within 10 days of coming in contact with hookworms so it's imperative to work quickly to find a solution. Adults, on the other hand, commonly don't have diarrhea at all so it might have otherwise been difficult to know there were issues. Also, in some cases of heavy infestation, dogs must stay on a constant 2-4 week dosage of dewormer to keep ahead of the cycle (this is uncommon, but I've seen it in a few locations). In these cases, even monthly dewormer at a regular dose may not be enough to rid an adult of their intestinal parasites. Again, rare, but it does happen and is possible it's happened here if the mother is, by chance, receiving treatment that is effective against them.
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