Bubble baths are underway. Dinner is made to order. The daily itinerary? Naps, training sessions and facials. Outside, a happy pack tears around fenced-in play areas as staff keep watch from offices overlooking the grounds. The guests are dogs. And this is their country escape. On a sunny afternoon at Far Fetched Acres in the Hudson Valley, one eager pup worked through a training session while others mingled in thoughtfully matched playgroups. Inside the custom-built, 10,000-square-foot postmodern barn, lavender-scented air sets the mood. Each dog has a personalized cubby stocked with food, medications, toys and detailed instructions from home. The...