I think you already got really good advice about the second opinion, but I would still be concerned about kennel cough. Our girl got it when she was tiny and the vet didn't think it was kennel cough at first either because when he tickled her trachea, it wasn't making her cough. But, he said we had better prescribe treatment for KC just in case (it was Friday going into the weekend and he didn't want her to get worse without treatment). Sure enough, he said if it was KC, her coughing would get worse before it got better with the antibiotics, and by Saturday night she sounded like an old geyser with emphysema--hacking, coughing, and sounding like she was gagging when she did. But, by Monday she was back to her normal, non-KC self. I'm not really about giving medications they don't need, but I wouldn't mess with KC, especially in a little one.
Hopefully you can get a second opinion as to what your baby's issue is, but like I said, I think you already got good advice here
