I think living wild for 6 weeks, assuming the vet has been all over the dog, is less of an issue than the dog being re-housed so many times. Living wild, then being found, now being in foster care, and now possibly moving to another state. Those are all stressors.
We rescued an 18 month old dog who had been ill cared for (no discipline), given up, adopted, returned by the 2nd family, put in a dog pound, rescued from euthanasia by a wonderful humane society, put with another little dog who got adopted which caused stress for the one left behind, and then she was put in foster care. We adopted her but we do not have little kids and we work at home so could provide constant care. She had some food aggression and a big fat fear of abandonment. We were approved because we knew her breed (she is a Cairn terrier mix and we had had a Cairn for 14 years). It took vigilance to get rid of the food aggression and a long time to integrate her into the neighborhood. She's now wonderful but still can't be boarded if we go away (which we've only done twice in 10 months) - we have to have someone stay with her in our house so she doesn't have to leave her home and be without us.
So, I would suggest that those puppies get vet clearance and then be given to some people who can visit them in foster care, take the puppy of their choice out for a few walks and maybe a car ride, and gently ease it into their own home and life.
If you want a dog, I would suggest you go to a local shelter where the staff knows the dogs and their personalities, their backgrounds, etc., and where there is a really thorough application process to help make the "match". You can visit, walk, play with the dog, have it get to know you, etc. These dogs all need to go to their "forever homes" with no glitches and no "giving them back if it doesn't work out", and it's really important, in my view, to not transport them over and over again. Many of my neighbors have rescued dogs from far away, and they are all so traumatized that they are loyal only to the family and can't interact with other people and other dogs. I'm talking 4 dogs in one neighborhood. Same sad story. If you have little kids, you are right that a scared dog is a problem. Those puppies might do better with a quieter household and fewer people to bond with - they will most likely need an authority figure and some calm, and a family of kids just doesn't provide it in many cases.
Good luck with whatever you decide.