The Westminster Kennel Club is set to crown the cream of the canine elite on one of tennis’ most storied courts next week. At the same time, another 19th-century institution across town will be tending to dogs that have had far more troubled lives. New York is home to both the United States’ most prestigious dog show and its oldest humane society, the American Society for the Prevention of Cruelty to Animals. Some proceeds from the very first Westminster dog show, in 1877, helped the young ASPCA build its first dog and cat shelter years later.