There are books written about hotels/motels across the country that accept pets. I know I've seen them at Barnes & Noble.
I'd probably talk to my vet with regard to healthcare. You'd probably need a copy of your pet's entire vet record, so that if, God forbid, something happens, you'd have a complete record of the kind of care and "issues" your pet has had in the past. I'd also ask your vet if he/she had any collegaues that they knew in the areas where you would be going/staying.That way, if something happened, you could feasibly say "Well, I am a patient of Dr. Soandso in East Timbuktu. He recommended I call you with any problems while I am iin this area".
I'd probably get the dog microchipped, as well as having ID tags with several different contact numbers on them. Your cell, your home, your son's cell, your son's home. When we had our Ted, I had 2 ID tags on him...one with my contact information and one with my parent's contact information.
I don't know how your dog is in the car, but we used to have Ted stay in his crate when travelling...keeping him contained seemed safer for him to us. We also always kept a leash on him and always made sure one of us had a hold of the leash before we opened the car door any time we stopped...this lessened the possibility of him "bolting" out of the car in a strange place.
Make sure you have enough of his usual food to last the entire trip...you never know if it might not be sold where you are going. Water, favorite toys, bed to sleep in.