The other mother : when a lesbian couple broke up, one of them learned how fragile the definition of motherhood could be

P. Orenstein

Parmesan refuses to go for a walk. The chubby yellow lab and her owner, K., used to go on long rambles through the California hills. But for the past year, Parmesan has planted her rump as soon as she hits the driveway. It has gotten so bad that on a spring Saturday morning, K. brings her dog to the Humane Society for a consultation with a team of animal behaviorists. The trainers feed and roughhouse with Parmesan, then clip on a leash. They walk beside K., the dog trotting along happily, then lag back as if they were going to leave. Parmesan stops cold. They try again with the same result. And once more. They also observe K., whose dark eyes are as large and doleful as her pet's.''Something has happened to traumatize this animal,'' one of them finally says. ''By any chance, have you experienced a loss?''Hours later, K. is still amazed. ''I can't believe they picked up on that,'' she says, patting the dog's head. The two of them have settled into the living room of K.'s town house, the one she moved to after selling the four-bedroom suburban home in which she, her lesbian partner, E., and the twins she very deliberately calls ''my daughters'' used to live. She feels safe here. The walls, carpets and furniture are an innocuous model-home beige, the coffee-table books -- ''The Century,'' ''The Spirit of Family'' -- similarly bland. The only zing comes from the photographs -- and they are everywhere -- of the two little girls. Here they are trick-or-treating as a bear and a tiger. And over here, posing with Mickey at Disneyworld. Over there, in a purple frame surrounded by butterflies, they're marching with K. in a preschool parade.