A fundamental problem with dual-arm robotic control is to find the coordinated motion resolution under high kinematic redundancy and intrinsic constraints of each robot. To solve this problem, this paper presents a multi-tasking, co-operative control framework, in which potential task conflicts and robot joint constraints are properly handled. Based on the relative Jacobian formulation, singularity-robust inverse kinematics and the scheme of null space distributing exceeded joint velocity, this work contributes by introducing a framework to handle multi-tasking conflicts both in task and joint space for dual-arm robots. Detailed validation of the proposed framework is first conducted by using a simulated dual-arm robot, followed by a demonstration on two 7-dof Kuka lightweight manipulators in a bimanual stent graft manufacturing task.