Have walked this route with my two collies some 4 years ago - but camped, so can't help with o/n accommodation. However these pubs welcome them - The New Inn at Appletreewick (But not the Craven Arms). The Kings Head, Kettlewell, The White Lion, Cray. The George Hubberholme. The Sportsman at Cow Gill (But not in the bar - only allowed in guest bedrooms!). The (I think) Anglers Arms at Burneside.
I assume most that allow dogs in the bar, also allow them to B&B?
Livestock abound along the route - take care, if your dog 'investigates' sheep, and be aware that cattle may 'investigate' your dog!
Also hundreds of ladder styles, which my older dog began to struggle on, after a few days of leaping down from 1 - 1.5m dozens of times a day.
Generally though - a pretty good walk for a dog to do! - Repeated several sections (and several pubs!) since on day walks, with both dogs.
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