I have to say that the dog friendly hotels being dirty is kind of a silly generalization. There are many 4 and 5 star properties that allow pets, as well as plenty of places with more modest prices that will still be clean. I'm sure there are plenty of mediocre places that accept pets, but I doubt the percentage is much higher than than of those who don't accept them.
As far as a 4-5 day loop that includes Route 66, I'd think you could probably get about as far west as Oklahoma City, head back east through Arkansas, and then make your way home via the Great River Road.