Dear Wayne, I don't know if it is a good idea to give your babies small doses of antibiotics. As Saversmont said, if there is a virus causing distress, antibiotics would be useless (they destroy bacteria only). But the point is that administering antibiotics in small doses or only for a short time is ineffective and even dangerous. If antibiotics don't kill bacteria completely (and that's only achieved by a regular dose for quite a long time!) then the remaining bacteria (those who survived the medicine) "learn" how to "fight" the antibiotic, so next time your cat (in fact, ANY cat) gets the infection, it will be more difficult to beat the disease. This is called Antibiotic Resistance - I've found some articles and sources on the Web, I post one from the U.S. Food & Drug Admin., though there are a lot from Europe as this is quite a hot topic here!:
http://www.fda.gov/fdac/features/1998/698_bugs.html
I hope you find this information useful!

But, now, MOST important, you seem very concerned about Snow, I hope everything turns right and you (or your vet!) sort out what's happening with the furkids! You have all my sympathy, please keep us updated!

Nita