Two-stage processing machines for manufacturing are equipped with two sets of actuators for motion control with different operating ranges and bandwidths. The processing time, product quality and flexibility of the manufacturing process can be optimized by coordinating these actuators and exploiting the entire actuator operating range. We propose a motion control strategy for two-stage processing machines based on model predictive control (MPC). By exploiting timescale separation, we formulate the problem as a single-stage motion control with reference-dependent constraints. Feasibility of the MPC problem is guaranteed by using a reference governor that adjusts the feed rate. The proposed method guarantees correct processing while satisfying the actuators' range and dynamics constraints, finite time processing of a given spatial pattern and real-time execution even with limited computational resources. Simulation and experimental results on a real processing pattern are shown for a scaled laboratory demonstration machine.