"Cabins" are becoming more and more popular in Indiana. But I have not seen a single one yet, anywhere, that provided bed linens and pillows. You have to supply your own. Motels would be much easier. Check on-line for "pet friendly motels". More and more motels are becoming pet-friendly. What they are doing is simply removing carpet and replacing with floor tile. Rooms are still comfortable.
Last motel we stayed in (last December on our way to Florida before getting out of the snow belt), the wife looked up dog friendly motels. Turned out the one we stayed, almost every room was occupied and every room had dogs. There was a dog contest going on in the area! Who would have thought. Our little dachshund had a fantastic time meeting new friends. But our cat didn't appreciate the accommodations at all! It was really an exciting moment when the cat got out the door of our room and started bolting down the hallway! Oh, EVERY dog in EVERY room knew there was a cat on the floor. The barking was hilarious, and we had one cat that almost stroked out!
Once we got the cat back, we put him back in the camper. He was much happier.