Moving with pets is an added consideration. Not a "problem". I travel with my 3 dogs frequently. Red Roof Inn always takes me if I call ahead. Not the Ritz, but I would rather be with my dogs at a Red Roof. Cudos to the craigslist poster. Pets are a commitment and too many people don't realize how much of one.
My pups are spoiled rotten. On the bed at a house I rented for January in Gulfport, Florida.
Speaking of dogs at train stations......have you seen the movie HACHI?