I had a litter much younger then yours develop KC. I've learned a lot since then. At the time I did not put them on Antibiotics though I did work with my vet and the cough was not nearly as bad as I have heard from others. They were fine. If God forbid it happened again, Clavamox I would use as you are. In your situation with already hearing congestion, you may want to ask your vet about Azithromycin Oral Suspension for them and see if they can get on it. That, or something similar. Also ask about a little cough medicine which some have used with a varied degree of success to surpress the cough. Good Luck and let us know how they do.
You need to keep them on antibiotics, you are correct a secondary infection is what to be afraid of. The antibiotics will certainly not cure the viral KC but can prevent secondaries.
Yes we have had KC in babies, ours came down with it around 10 days of age. Our vet put them on Amoxy but they still came down with a sinus cavity infection which was very tough to deal with as the antibiotics would not penetrate the sinus wall. It had to be administered directly. All 11 puppies ended up fine.