Yes, I would speak with the boarding kennel or try to find a pet friendly hotel. You might consider a pet sitter that will come to your home. Best if they are bonded. Your Vet or pet store may have recommendations.
I do not really advise leaving her in the car fir a number of reasons.
My vet boards our cats, but even with a small dog like this, they don't.
What about your Vet clinic? Your VET has boarding facilities and they are not kept together...Everyone should have a separate kennel.....
I'm going to try the local place, and have a long talk with the owner first. They are only two blocks from where I live and maybe could even meet her at home first. Thanks for the suggestion to talk it over with them, I just was not sure they would even hear me out. (They say all dogs should be "well socialized." And she is, but can be so weird in boarding settings.)
see if the area where you are staying does doggy day care, see if the hotels allow pets!! Its too hot for a car!!!
Be honest with the boarding facilities, as I have worked with MANY, they can refer you to a place or put a sign up and take special precautions. I was bit by a chiweenie and a palmchi its OKAY they know it can happen, I dont know your states laws but being HONEST is the best bet!! if not can a friend watch them?