What kind of shampoo did you use for the bath? I'd suspect a bacterial skin infection that a bacterial shampoo might help. You don't want to shampoo too often but one more might help. Just as important is to rinse thoroughly. If you think you've got the shampoo all out, rinse twice more anyway. Also just as important is quick and thorough drying. I use a blow dryer, the same one for my own hair. All that goes for the collars as well, I'd make sure to wash them too, and dry them with heat, assuming they are nylon. I now use a waterproof betathane collar and it's only on for walks. You also need to treat all their bedding the same way.
I tried five shampoos for Oban's itchy allergies till I found this one that worked for him.
Access Denied
You are in the U.S. so you might be able to buy a dog shampoo that has chlorhexidine in it off the shelf. Here in Canada it's a controlled substance and only available through a Vet. This is ingredient was suggested to me by more than one board person on a couple of boards so it seems to be well regarded. The shampoo I do get (link above) is close I think and only available to me at a horse place.
If shampoo doesn't work then I guess you'd have to address internal issues. It seems unlikely two dogs would both develop some kind of illness that would cause this in both of them, but maybe you could at least ask your Vet. They might have seen others the same and at least have some other options for you to try. Good luck.
ETA: Probably it's obvious but don't wash and rinse with the lake water. If you are still at the cottage maybe the water you drink would be ok.
ETA: The link works but just in case, it's Furrever Devoted Medicated Dog Shampoo