Integrated modelling of spacecraft roto-translational relative motion is an emerging topic of interest for multi-agent space systems design, analysis and control. Dual-quaternion is a satisfactory solution to this complex problem. Model Predictive Control (MPC) is, on the other hand, a powerful model-based control methodology with known superiorities over other modern control approaches used in the field of spacecraft control. Embedding the dual-quaternion model in the MPC approach for sophisticated systems, thus yields a valuable control framework. There are, however, some difficulties involved in this proposition that need to be addressed. This matter is scrutinized in the present work. To this aim, the concept of dual-quaternion and relevant tools are first reviewed. Subsequently, potential interfaces between dual-quaternion expressions and MPC framework are highlighted. Accordingly, a piecewise affine MPC scheme based on the dual-quaternion model is introduced and further developed in several aspects for space roto-translational relative control missions. First, it has been improved for zero steady-state error. Furthermore, it has been developed to explicitly deal with reaction wheels as attitude actuators, in terms of limitations as well as related costs. The efficacy of the proposed integrated scheme is assessed by comprehensive simulations.