Smaller towns often don't have hotels. Motels are not as ubiquitous as in the USA. Most economical accommodations are near bus stations and the next choice would be in 'centro,' downtown, where you would be close to activities, shopping, points of interest like museums, churches, etc. Except in areas popular with expats, real estate and rental agencies are rare. You will have to ask about rentals in small towns or look for them in classifieds in large cities.
Be sure you know about the temporary importation of your car and your responsibilities for removing it from Mexico, no matter what, and for Mexican insurance.
Mexicans do NOT travel with animals and they are NOT welcome in the majority of hotels or rentals. Even those folks traveling to a single destination have trouble finding a place to stay with animals when they have to stay a night or two along the way. I couldn't imagine trying to enjoy a vacation with even one of our dogs. It won't be able to stay in the car because of the heat and will not be welcome in restaurants or any other place you might want to visit. I really would suggest that you board the dog while you travel or hire a dog-sitter to stay in your home. In general, dogs are watchdogs here, not house pets, and are quite expendable in many cases.