I'm sorry I don't know the symptoms of kennel cough. Have you searched the internet for any info? Is Buttons on heartworm medication? I know one of the symptoms of heartworm is a rasping cough or trouble breathing. I'm not familiar with Buttons, I'm sorry. Did you get her from a breeder?
It seems like the vet would have given her a kennel cough vaccine especially knowing she lives with 2 other dogs. Do you get the others vaccinated against it? I know it's every 6 months and my vet recommends it if you go to any dog parks and requires it for kenneling.
Good luck! I hope buttons is OK. I love bassets, they are the cutest dogs!