Assistive robots have the potential to support independence for older adults with mobility limitations and to alleviate the demands of their care partners. Several design considerations are required to ensure that the users can successfully rely on the robot to carry out their tasks. Therefore, building trustworthy robots is necessary for wider acceptance of these assistive robots. Using a participatory design approach, we assessed various aspects involved in advancing the design of a trustworthy robot in home environments. This is a case study focused on supporting an older adult with mobility limitations and his care partner. Through several iterations of co-active development as a team, most of the tasks were accomplished to meet the needs of the older adult couple interacting with the robot. Our approach highlighted usability challenges, the merits of a multidimensional approach in evaluating trust, and co-design strategies to improve the trustworthiness of the robot.