Maybe have them keep your dog in a room away from the other dog.
Try to keep your dog away from the other dogs as much as possible until your pup is vaccinated. My pup had kennel cough too and was around my parent’s adult dogs and they didn’t catch it but better safe than sorry.
Their dog (and all dogs who visit other places often, IMHO) should go in for a bordatella vaccine. It isn’t a shot anymore - just a nasal spray.
Good luck!
Some strains of kennel cough can persist for 2-3 weeks after the dog has completely recovered. I would recommend leaving your dog at home with a pet sitter, or if you absolutely must take him, keep the dogs separated and make sure the other dog has had a recent bordatella vaccination - though the vaccine does not cover all strains of the disease. Honestly, if you were visiting me, I’d nicely ask that you leave your dog home. Not fair to expose other dogs.
Has your dog completed her round of antibiotics? My pup currently has it as well and the vet said she can be around other dogs again 4-5 days after the cough has completely subsided. Your relatives could re-vaccinate their dog, but it needs to be done a couple weeks in advance. I think your only options are to take your dog to your vet’s for boarding, get a pet-sitter or reschedule. You can try completely isolating your dog once you get where you’re going, but that’s not really fair to her.