On the Far Side of the Mountain — Jean Craighead George

Two years after Sam Gribley first ran away to live off the land, he is still on his own with his falcon, Frightful. His independent younger sister, Alice, lives in a treehouse of her own nearby. But suddenly, Sam's peaceful life is shattered. Frightful is confiscated by a conservation officer, and Alice disappears. To find them, Sam must leave his mountain refuge and track Alice across the Catskills as only he can do. The trail to the far side of the mountain may lead Sam to the two beings that matter most to him -- or it may lead him into grave danger.