She couldn't have caught it second-hand from the vaccine but it is possible that the pup brought it from contact with the other dogs, though since it is airborne transmission, it is unlikely. Many dogs do however carry the disease and yet show little or no signs. Incubation period is 5-10 days before a cough is seen. If the dog coughs in response to the pressure, more than likely it's kennel cough. Treatment for the disease is usually minimal - like human viruses, it must simply run its course.
Most vets treat the dog with an antibiotic to prevent secondary bacterial infections.
Most good vets will tell you that there is really nothing one can do to cure the disease. Vaccines are good for preventing the majority of cases. Dogs with a lot of exposure to other dogs should get biannual boosters to be safe. But just because a dog is vaccinated does not mean it cannot get kennel cough. Like human flu shots, the protection is against most, but not all infectious agents.