While I’m not traveling that route, I do travel often for dog shows. Even in the hotel brand there can be some differences based on the franchisee. Best to check each hotel either on their brand website (not like expedia or booking.com), or call directly. Motel 6 is usually a safe bet that they are ok with pets, and AKC offers a discount code for 10% off (CP542764). However, there is usually no wifi.
I really like LaQuinta as a chain for accepting pets when I can get the room priced decently.
Also, be aware that some hoteliers will force customers with pets to be in a smoking room.