Mobile bimanual manipulation in a dynamic and uncertain environment requires the continuous and fast adjustment of the robot motion for the satisfaction of the constraints imposed by the task, the robot itself and the environment. We formulate the pick-and-place task as a sequence of mobile manipulation tasks with a combination of relative, global and local targets. Distributed distance sensors on the robot are utilized to sense the surroundings and facilitate collision avoidance with dynamic and static obstacles. We propose an approach to kinematically control the robot by solving a priority constrained optimization problem online. Experimental results on the YuMi bimanual robot mounted on the Ridgeback mobile platform validate the performance of the proposed approach.